In my opinion, the supply cap is not enough to guarantee that bitcoin will rise in price and hit a new ATH, it is more important about its demand. I mean, even if bitcoin has a limited supply but its demand is not high, people don't value it, it can't go up in price. Supply and demand need to work together, higher demand than supply is enough to trigger higher bitcoin prices in the future. So, whether bitcoin goes up in price and hits a new ATH is entirely up to us.
Sorry for the late reply, but I'm short on time at the moment. Yes I agree with you. Certainly, capping the amount of bitcoins is not the main reason why we will eventually see a new ATH. As you write, supply and demand are the main reasons for a new ATH. But by limiting the amount of bitcoins, this could also lead to the supply of bitcoins becoming very low in the future. Surely the demand still needs to be high to hit a new ATH, but maybe the limited quantity will help with that. Either way, I see the limit as a good thing and it's an advantage that hardly any other investment or currency can offer. 
This is why I believe that we should not really be doing something like this at the moment, what I believe however is that if we could get bitcoin higher, then the cap has "something" to do with it. Obviously when you look at ETH and how it is unlimited, that still goes up and we are doing fine about that, which means that it's not the only reason and would never be considered that way at all.
Yes, ETH is an example of this as it has an infinite supply. As I also said, supply is not the deciding factor, but demand determines the value of bitcoin, and we are the creators of that demand. But limited supply combined with high demand will help bitcoin reach its maximum value, and that is also why ETH has a very high value, but it has never surpassed bitcoin.
The combination of these 2 can answer OP's question is bitcoin will still have a new ATH because the demand for bitcoin is still increasing day by day while the supply is limited.