Unless your character is meant to be The Undertaker or John Cena you should be fully willing to tap out to a submission. I'll never understand the idea of tapping out "damaging your character". It's the complete opposite. There's a reason old school heels always had submission finishers.
Watching a babyface you're really getting behind tap out is heartbreaking. It makes you root for them getting their own back even more and gets the heel over. Meanwhile, having them pass out makes them look tough and resilient.
On the flipside, having a heel tap out is a sign of them getting their comeuppance. If they've really been getting under the babyface's skin and they're forced to submit then it gets the babyface over.
No matter how flashy or complicated wrestling seems to get, one thing always stays the same (including in efeds): The aim of a match is to get someone over. The other person/people should always be willing to help them because, in the end, they all benefit.
TL;DR Submission finishes are a great storytelling device and I'd be more than okay with tapping out.