Browser engines define the capabilities of web apps and websites. When they don't support APIs or have bugs, they impact negatively web software.
Apple's WebKit is renowned to be lagging behind, refusing to implement crucial features and being rigged with bugs, hence limiting the capabilities and quality of web apps, and effectively preventing them to compete with native apps.
Getting other browser engines on iOS would be beneficial for developers, businesses and end user by making mobile web apps viable.
To be fair to Apple, as a user of Safari, I mostly agree with their feature omissions. Web developers have shown near limitless capacity for abusing new platform features and Apple has provided sound explanations for why they won't implement eg. web bluetooth. On the other hand as a web developer I have definitely suffered my fair share of Safari's incompatibilities (however I find myself in these situations less and less these days).
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.
Apple's WebKit is renowned to be lagging behind, refusing to implement crucial features and being rigged with bugs, hence limiting the capabilities and quality of web apps, and effectively preventing them to compete with native apps.
Getting other browser engines on iOS would be beneficial for developers, businesses and end user by making mobile web apps viable.