It is related only to WebKit (Safari). So I think people will just switch to other browsers.
Except for iPhones/iPads where you don't really have a choice. Also most people don't give a shit which browser they use, they just use whatever browser is available when they get their device, which makes sense. But those users might soon have their data removed without really understanding why.
I am the creator of a photo editor www.Photopea.com and I see, that more and more people care about their browsers. They spend a lot of time discussing the issues of their browser with me, because they need to do a serious work in it.