As time goes on in 10, 15 or 20 years, bitcoin will get exponetially harder to mine and to recieve rewards.
This is not true.
You spend some more time learning about how it is that Bitcoin actually works if you want to make statements about it's technical merits.
I think this is an inherent design of bitcoin
It is not.
with a supply cap.
Yes. Bitcoin has a "supply cap", but that cap has nothing at all to do with how hard it is to mine it.
It will be reasonable to assume, miners will eventually go away to other easier to mine coins.
If there is less hash power working on bitcoin blocks, then bitcoin blocks will become easier to mine.
The difficulty is set based on the amount of time it took to mine the previous set of 2,016 blocks. If it takes too long, then difficulty drops. If it happens too fast, then difficulty increases.
Who will then maintain the bitcoin network and keep it going?
The remaining miners that are more profitable when the less profitable miners leave.
How will bitcoin maintain its value?
Through increasing demand for its functionality and usefulness.