The last BTC will be mined in approx. 2140. But the change is not going to happen overnight. There are a lot of factors that may change within this period, giving miners time to adjust to the new rewarding system and for the BTC network to remain secure. In more than 100 years from now, it seems likely that all these issues will have been solved by Bitcoin Core developers and the wider cryptocurrency community.
I do not think that there is problem with the system that pays miners from tx fee. I believe it is already happening, Miners compete for the new block and mine the block together with the tx fee. There is no need for the miners to adjust, they just need to point their miners and hash away, solving blocks and mining tx fees.
I think by that time, the scalability issue will be solved.