In the case of bitcoin cash in particular; it would probably still be fine at bitcoin scale. This is because its main difference is removing an artificial limit within Bitcoin. As this limit was set without an empirical basis (and bitcoin showed no signs of degradation as it approached the limit), you would probably be able to scale the block size up some without causing problems.
How much you can scale is still at question. Here [0] is a talk about this very question. Using a small testnet (~6 miner nodes and 12 clients) they were able to achieve 500tx/s with a 1GB block with relativly minor optimizations of the standard Bitcoin implementation (the final bottle neck here is propagation delay reaching 10 minutes). This is, in my opinion, an upper bound on what the Bitcoin protocol can handle.
Smaller transaction sizes with adaptive block sizes seems like a good scaling solution. Is there something I'm missing?
The fee in terms of XMR actually reduces when there's more transactions. However if its value in terms of USD rises, then the fee in terms of USD still might go up with more adoption. Perhaps that's something the developers can adjust in their regularly-scheduled hardforks.
That still makes it a little larger than the average Bitcoin transaction, but the mentality there seems to be that privacy has its price. While next-to-free is preferable, I don't disagree.
This isnt future proof but should alleviate some pressures while internet and widespread computational infrastructure improves
Monero’s tx fees are low due to lack of use, they go up way faster than bitcoin’s even with RuffCT and adaptive blocksizes.