By 2140, no more Bitcoins will be created so people will probably move on to other crypto currencies.
This sounds consufing.
You mean miners move on to other crypto currencies, since they have too or people (speculators) etc.?
Fees will most likely be miners incomes, since block reward would be so low.
I think that bitcoin would still be as profitable as it is today. it takes just one big bitcoin farm to 51% attack a sha-256 altcoin. So they will most likely move on to new algorithm. Most likely my bet would be that PoW coins will be superior only to some point in the future. Beyond that point PoS or other methods would be far more superior.
At present, PoW is the most fair and efficient way to distribute the coin for long time. In PoS coin, the coins are distributed in one go (ICO) or very short period. So it is unfair to later comers as the only way they can get the coin is to buy. For the PoW coins, you can buy/rent rigs to mine. You can also buy cloud mining service.