It's good odds that banks and streaming services are scrambling to implement it as we speak. You know they are. DRM is the perpetual wet dream for the music & film industry and for streaming services. And banks are paranoid as a matter of course.
It's going to be very hard to say no, especially since they can say "but Chrome is working on all platforms, nobody's pushing you out of anything". Will you drop stream subscriptions? Everybody loves to say they'll drop Netflix "as soon as they push me one more time", but what about a service you actually like? And what about banks, are those as easy to switch?
I've been through this for years now with Android and SafetyNet and it's a lot of hoops to have to jump through to stop being considered a second class user on your own device. It's going to suck extra bad when it comes to PC.
As for Google services themselves, I'm very curious to see in what order and how they choose to make WEI mandatory. Maybe not for Search and Gmail, at first, but what about accessing your Google Account, surely that must be secured? And YouTube of course, that's got DRM written all over it.