Bitcoin ETF was expected to partially tackle the No. 1 problem by increasing adoption; the more demand, the higher the price increase.
Well, yes, but in theory. I mean it is expected to let people know about bitcoin, but not to increase its value if people buy shares of the ETF.
Imagine the ETF provider A, who owns 1,000,000 (1M) bitcoins and they provide 1,000,000,000 (1B) shares to the customers.
So we have 1B shares of 0.001 BTC each.
Theoretically, they are not allowed to trade the underlying asset of the shares that belong to customers. They are allowed, however to sell Bitcoin that is not sold (in the form of shares to customers), or buy more bitcoin and create more shares.
So, the actual trades, that would lead bitcoin's price higher (or lower) depend on them.