Mining uses quite a lot of energy, this will show up as transactions fees
Wrong. If mining takes up too much energy, mining will become unprofitable, some inefficient miners will quit, and difficulty will fall until energy costs are in line with mining profits. You've put the cart before the horse here.
What I mean is that if you compare two cryptocurrencies, one which uses mining and one which uses proof-of-stake, then the one which uses proof-of-stake will eventually be cheaper to use for the users, since the total cost of running the network will be less. Around 2030 or so, when the majority of bitcoins are mined, unless the value of a bitcoin is high enough so it's still worth mining just for the block reward, it might be cheaper to use proof-of-stake or something similar. If bitcoin then do not change to proof-of-stake, or another system not based on proof-of-work, perhaps that eventually might cause bitcoin to collapse, if there is a good alternative available and people gradually start switching to that one, and then that gradual switching suddenly lead to a panic and collapse, just speculation of course, but I'm keen to know what the options are to avoid something like that from happening.