If you stop mining bitcoins, anybody with a small rig can produce a double spend and destroy all trust in the network. It wouldn't disappear, but the coins wouldn't be worth much.
Proof of stake would solve that?
But then you're no longer talking about Bitcoin.
Bitcoin is whatever the majority decides... They could also increase the supply if they wanted to, or whatever other change comes to mind? Think of it as Bitcoin 3.0, 4.0, etc...
Changing the block size was so controversial that it split the community and created years of bad blood and claims of shilling. I don't believe that the core devs are capable of making such a huge change as moving to PoS.
If no more bitcoins were mined, you couldn't move bitcoins around. You can only include new transactions by mining a new block.
Isnt that one thing that the lightning network can solve?
Ultimately, you need to be able to settle lightning transactions on the actual chain.
It could move to the exchanges moving around IOUs. It's not like actual gold moves around every time I buy some on the internet, someone just moves data in a giant excel somewhere.