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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.
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