And that is the more reason why we don't need to expand or increase the total supply
Bitcoin Cash does exactly that (even if it is not a true Bitcoin)
The lower the supply, the higher the demand and that also means the higher the price of it
The latter doesn't necessarily follow from the former
It works wonderful with valuable things that cannot be (easily) substituted with similar things performing the same role or function, and in that case a decrease in supply translates directly into an increase in demand and price (sometimes even with a vengeance). I'm not sure if this is the case with Bitcoin as its volatility prevails over any changes in the total supply (cp. the change in supply over the last couple of years with the price swings we see almost daily). In simple terms, it is more complicated
Apart from that, there is another factor which should be paid precious attention to, and that is utility. If utility goes down along with supply (a possible scenario), then the rise in demand is not guaranteed at all (so neither is the price). In other words, Bitcoin may become so rare that it may lose all utility it might have, and then it will quickly deteriorate and turn into a worthless asset (also a possible scenario). The same thing is going to happen if someone buys 99% of all bitcoins, just in case
Now such ideas seem completely out of place (and time) as Bitcoin is not serving the world even in its present state. Sorry if this is not what you wanted to hear but it is better to see what is really going on, however unpleasant it might be. Other than that, what you suggest is what altcoins already do, effectively expanding Bitcoin's supply
There's no point in any of us guessing where it's going to end up. It's early days still and anything could happen. This current period is a phase that'll pass. There'll be many more users who'll find many more uses
I hope you are proved right in the end
Yet, Bitcoin has been in the spotlight for at least 5 years by now, so you can't possibly say that it is "early days still and anything could happen" (people had been telling that in 2013). Indeed, anything can happen (regardless of maturity) but if nothing particularly good happened in the last few years in terms of "many more uses" (more specifically, uses not related to trading and gambling), it leaves plenty of doubt whether and to what extent things are going to change in the future. So what is going to change that didn't or failed to change already?