Edit: Can't reply further, but the way of doing this is much the same as installing unsigned apps on an xbox. Using a (free) developer account you can sideload things quite easy using something like https://github.com/ios-control/ios-deploy
Anyone who pushes Web Apps as a viable option is being disingenuous about what it provides or purposely ignorant.
Edit: So the only way to do it besides jailbreaking is for literally everyone who wants to do it to pay Apple an extra $100 on top of what they already paid for their iDevice. (Sharing will get your certificate revoked.)