Why many startups use IAP for their iOS apps, while they could direct the website to buy premium? Many startups offer their premium version both via website and IAP. Lumosity is the example of such app. 

I know IAP is made for such cases, but since you can upgrade your account on their website, why do they use IAP and pay commision instead of redirecting to website to buy premium?

Is it mandatory in iOS app that you have to support IAP for premium version even though user can upgrade his account via the website?

I'm curious because in IAP commision is 30% while costs of operation on website are much lower.

I mean, does these startups pay 30% to Apple just to allow users to unlock it from the app, instead of showing the message "Please visit our website to upgrade to premium version"

What if someone has upgraded lumosity through their website - he doesn't have to use IAP, he just logs to the app and new features are available right away.

Does that mean the following? I run a SaaS product with price tag 50$/month. If someone pays me via my website, I'm lucky, my operational costs are low. If someone decides to upgrade via the iOS app - I have to accept 30% commision fee.
Yes, it's mandatory. Per the App Store Review Guidelines:


  If you want to unlock features or functionality within your app, (by way of example: subscriptions, in-game currencies, game levels, access to premium content, or unlocking a full version), you must use in-app purchase. Apps may not include buttons, external links, or other calls to action that direct customers to purchasing mechanisms other than IAP.


Some services absorb the IAP premium on behalf of the user, but I've certainly seen some services that just charge 30% more to subscribe/upgrade within the app, than they charge if you do it directly on their website.