But I don't think anyone is arguing that we should stop mining new blocks
I didn't say that we should stop mining. I said 'after' means when 'there are no blocks left to mine, may be in 2141.
In that scenario, can Bitcoin ossify?
There will always be more blocks to mine as long as someone wants to mine them. If people stop mining blocks bitcoin ceases to exist.
Why would people mine when all 21 million Bitcoins are mined?
Transaction fees.
Think about this: how do you use bitcoin? How do you pay someone with it or receive it? A transaction has to get included in a new block.
If no new blocks are mined, no bitcoin can move. What is the use of a money that cannot change hands?