The likely outcome of alternate, capable browser engines coming to iOS will be to push Apple to invest in Safari so it can compete with them and not loose all of its market share.
Otherwise, yes it's likely web apps will prompt their user to use a browser with a capable engine on iOS if they exist. Nothing to configure, install and use.
Users will then be able to use capable web apps that take up a tenth of the storage of native apps, that are cheaper and portable across platforms — among many other benefits.
On my Mac, Google Chrome takes 1.8 GB. I would be pretty sore if I had to download that on cellular while trying to hail a cab in a foreign country because the app requires something like the Battery Status API in order to extract a surcharge because my battery is at 2%.
People were accusing Uber of this 10 years ago. It's not a secret concept. And while it seems Uber has never actually done this, it wouldn't surprise me if there are companies out there who do.