Why many startups use IAP for their iOS apps, while they could direct the website to buy premium?
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.