So no, you can't choose. When we say "you can choose" we need to realize that this is only good when you can make an educated, informed choice. If you can't, you need to be protected. And that's Apple's role.
Random choice is not a choice. Would you have your infant "choose" what drugs to take for headache for example? What criteria will they use? Pill shape, color, size and flavor. Well that's basically also our proverbial mom and pop picking a browser engine.
Furthermore browser engines have this peculiar habit of getting into everything. Open any app at all and it's probably using WebKit without you realizing it. What if the app uses some random outdated fork of Netscape, why not? Do you realize what "choice" you made by opening that app?
No.