Though, if SE built in parsers into ex trials and savage, that would probably be a pretty clear indication to people that those are only content that should be parsed. Would likely mean little to no parsing in any other content.

Of course that would require SE to build parsers as good as the existing ones, which there's no guarantee. If they weren't as good, ppl would just use the 3rd party ones anyways. And to make something as good as the 3rd party ones would take dev time, which would take time away from other things, further cementing a dislike of parsers.