The point about online banking is a bit dubious, but all my banks have decided that the Android app may conduct online banking alone, and it may verify a desktop session; but not the other way around.
I can only assume the Aluminium OS would aim to do the same
Social apps, messaging apps, parking/dedicated payment apps also tend to have miserable web support.
Oh, maybe the browser, so we are back to ChromeOS.
Chrome OS was already supporting windowed android apps, I'm typing this on the experimental desktop mode for Pixel phones, and it's not ready for prime time but it's usable enough. I could totally see a refined version of it.
What Google will do with the linux subsystem that was available on ChromeOS is the more interesting part IMHO. Do they just ignore that part or do we get something equivalent.
The point is that almost any windows/linux/Mac desktop application handles it much better than Android apps, which is what the question was asking.
There is a robust mobile gaming market worth hundreds of billions in USA alone.