The real justification for browser engine restrictions is not battery life but security.

If you look at any iOS vulnerability reporting, Safari is a big weakness and often the source of zero day attacks. Browsers are hugely complex pieces of software with a lot of attack surface. A large part of Apple’s value proposition is being secure. It sounds like the new approach (in the EU only) that allows additional browser engines requires specific security measures to be taken.

Rightly or wrongly device security is going to be a strong defense Apple has against some of these allegations.