(Actually that's a deep, political question, but I'll answer it neutrally)
Why is this? Why don't we remove the size limit?
As Nate Elredge said, miners can create free transactions. RIP Blockchain.
The limit also protects the blockchain from spam attacks - the dust transactions stay in the mempool.
It sounds like a simple problem that has a easy solution
Hard forks. It may take until forever to wait for people upgrading their nodes compatible with the HF. Also SegWit is a clever trick: "block size increase as a soft fork". In the future, the witness blocks' size can be increased so that Bitcoin won't need a block size increase anymore. (Actually this needs another complex trick, like SegWit)
Wouldn't miners make more coins from the extra fees from the extra transactions in each block?
Nope. If blocks were bigger, the users would set lower fees and the miners would earn the same.
What our are other solutions?
Schnorr. A signature system that is much more size (bytes) efficient. This would require a hard fork (or another soft-fork trick), but would work. Or as I said above, a newer version of SegWit that increases witness block size. Or maybe FlexTrans, a compressed transaction format (It looks like Bitcoin won't have it.) Or the most likely one: Layer two solutions: Lightning network, Liquid... They'll allow low fee instant payments, while keeping blockchain size low.