Have you clicked on a popular account but it's blank? This is possibly because your server hasn't "noticed" it yet. If you follow it, your server will show all their future posts from that moment on. (More info at: https://fedi.tips/why-does-someones-account-page-look-completely-blank-is-it-really-blank/)

But, it would be nice if servers could automatically show some past posts too!

This is called "backfilling" and is the most requested feature on Mastodon. If you're comfortable using Github you can vote for it by giving a thumbs up at https://github.com/mastodon/mastodon/issues/34