As the other commenter said, there is about 1 MB of room in each block, and almost always >1 MB worth of transactions in the "mempool" (actually it's often >12MB for the most part, because people will make tons and tons of transactions at 1sat/byte and not really care if they take forever to go through).

And you are correct that bitcoin's ultimate goal is to have mining income come solely from transaction fees eventually. But by that point the hope is that "second layer" systems will take the brunt of the transactions and the actual core blockchain will only be a settlement layer where a $500 fee is no big deal for 2 banks settling hundreds of millions of dollars directly on the blockchain.