To a certain point, it does (or will) already via Apple Pay and Safari.
But, while I answered yes, I'm on the fence. So far as I've read, the bar should provide shortcuts or make it easier to use any specific feature the developer feels is appropriate for that space. So while a back button, close current tab, print, etc... might be useful - how useful might it be to put a login or register button, or next article button, or up-vote button, or etc... Too many interfaces might be equally confusing as they might be useful.
You're also trusting web developers to produce good, easy to read / touch graphics and the web just isn't like that. There are websites with great UI / UX and then there are really crappy ones.
The more I think about it - it might not be a bad idea - would be cool if (for example) espn showed sports scores on it or an investment site showed stock ticker prices or news.
It'll be worthless (as Apple Pay is) if only Safari supported it and Chrome or Firefox didn't.