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Ranked Choice is inferior to STAR Voting in every way. 
RCV: rank top 3 preferences. If #1 is under say 50%, remove lowest count candidates and add your #2 to current count. 
STAR: give 1-5 points to every candidate you like. Add them. Runoff. 
That's it. It's simple to count, simple to analyze, simple to scale up. 
What happens in an RCV audit? You have to redo the computation. What if you have 150M votes? You need full strings for every single vote. No predictions are accurate. You can't trust national reporting as votes come in. 
And worse, RCV has a spoiler effect. Because your #2 only gets your vote if your #1 loses, #2 can lose an election because your endorsement of them was held hostage. Strategic voting is to only vote for popular people. 
STAR doesn't care. STAR is add the points up. It's simple. It's something you can update hourly and anyone across the world can understand. Big number wins.
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You are correct that IRV is somewhat better than FPTP for all the reasons you mention.
However, it is only slightly better.  In real-life elections with single winners, it tends to mimic the outcomes and problems of FPTP, especially in terms of heavily favoring a two-party system.
There are much better systems available that have all the benefits you mentioned, but much more strongly, and with less weird behaviors and distortion of outcomes.  Condorcet and Borda count are the most technically optimal methods, but they're a little harder to implement and explain; Approval voting has basically the same outcomes while being very simple and easy to implement, and is probably the best system overall.
Everyone should be aware that the reason the existing two-party structure has been pushing IRV really hard is that it also favors and recreates the two-party system in the way that FPTP does.  Basically, they are co-opting the movement for voting reform and turning it towards something that still favors them, instead of something that would break their duopoly and reduce their power.
People should not fall for this, and demand that voting reform efforts be channeled towards things that are better than IRV, and that will actually shake things up.  Again, I suggest Approval voting as the best method everyone should get behind. >

Ok I came into this post ready to defend ranked choice but thanks to you I can see I didn't actually know as much about it as I thought I had. I also hadn't even considered there were other, better options. Thank you for this, it is very informative. 
!delta >

Thanks, it's really a fascinating topic!  That paper I linked is a good place to start learning about it, and if you google the different voting methods mentioned there you can find tons more information and research about them.  Good luck! >

Thanks! This is why I love this subreddit >

Have you considered MMP? In MMP, districts are expanded so that there are multiple seats in each district, which are then assigned proportionately based on the percentages of votes secured. Let's say a new MMP district looks like this:
Right (60% total)
20% MAGA
30% Republican
10% Libertarian
Left (40% total)
20% Moderate democrat
10% Progressive
10% Socialist
Assuming there are ten seats per district, each party gets at least one seat. But, with no party having a clear majority, there are several possibilities for a coalition. You could feasibly have a right MAGA/Lib/Rep coalition, a moderate Rep/Dem coalition, a leftist Dem/Soc/Prog/Lib coalition, etc. This system essentially forces different parties to cooperate and compromise to find a solution to political problems that are, at the very least, acceptable to a majority of people. It has all the benefits of RC, but goes several steps further to enable a more representative democracy. 
To address your points: MMP is more effective at promoting third parties than ranked choice, and often forces multiple parties to rule by the coalition, thus mitigating the "winner take all" consequence of FPtP or RC. 
MMP does not require multiple voting rounds and allows for new ideas to be integrated directly by the parties that advanced them initially, rather than relying on these ideas to trickle into the agendas of mainstream candidates. >

A) That's not MMP, that's PR. MMP is what Germany uses- some members are elected from single-member districts, while others are from party lists.
B) Neither system works for single-winner offices like the presidency or governorships. >

I'm assuming you know all this, but I'm just leaving this here for anyone that's interested (I nerd out over voting systems a lot)
To put a finer point on this, Proportional Representation (PR) represents a class of voting systems that satisfy a mathematical condition called Proportionality for Solid Coalitions (PSC). Mixed Member Proportional (MMP) satisfies PSC and is therefore a PR voting system.
/u/dean84921 described a PR system that isn't MMP because it doesn't have the "mixed" element; part of the body being elected is elected through one method, and the other part has its seats distributed so that the entire body is proportional. Germany achieved this through having 2 MPs for each constituency; one elected through First Past The Post (FPTP, most votes takes all, AKA one of the voting systems whomst is bad) and the other selected from statewide party lists to ensure the Bundestag is proportional to the party vote. In the UK, where we call it the Additional Member System (AMS), Scotland, Wales and London elects local representatives through FPTP and regional MPs through a party vote, which is used to make sure the party distribution in the assembly reflects the part vote as best as possible. >

This still runs into the same problem that ultimately, you’re electing a single candidate for a specific district/region/whatever, who doesn’t really represent a potentially very large minority of the voting public. In, say, US congressional elections, you could still end up with all districts going to the same party even when a sizable minority in the state doesn’t support that party (and it is also very vulnerable to gerrymandering). 
Proportional representation is a better system. >

The problem I have with proportional representation is the selection style of candidates.
How exactly could you do that in a fair manner? >

The problem with proportional representation is they make bigger delegations. New Zealand has multiple representatives per district. Australia has 12 Senators per state. You can do that kind of thing with populations in the 7 or 8 digit range, but countries with a large population are more limited to what they can do without also radically overhauling the way electoral districts are allocated. Not saying they couldn't or shouldn't do it anyway, it just increases the complication factor, which generally people are loathe to take on. >

For Wyoming to have even 2 representatives, there would need to be 811 representatives total. And double-member districts aren't very common because it just guarantees a seat for the top 2 parties- which are mostly just the two largest ones. For Wyoming to get 3, there would be 1,405. 
The logistical problems with a legislature that large should be obvious. >

I do not see any insurmountable or even moderate logistic problems with paying a few extra salaries. More representatives means each one has proportionately less to worry about and needs fewer resources to get the job done I would think. 
What are these obvious hurdles I am missing? >

Communication amongst the delegates at large becomes more difficult as the number rises. Debate becomes more difficult. Finding consensus becomes more difficult. Housing, staffing, parking, office space and equipment, etc. It's quite a bit more than just a few extra salaries. >

Communication becomes easier when your representative has to speak for fewer people. 
Debate in the U.S. House of Representatives is already a joke. 
Consensus would work just as it does now. Get a majority and let the outliers make protest votes to appease their personal constituencies. Getting 2181 votes is not that much more difficult than getting 218 when the vast majority are voting the party line anyway. 
Staffing can be reduced when an individual representative needs to personally do much less. Offices and equipment can be rented. 
Housing and parking? I should have to share a representative with over 700,000 other people because of housing and parking? Come on man. These complaints are pretty damned petty when talking about how to properly represent 332 million people.