Hi Jack,
Boy, that's a really loaded question. iPhones after the X mostly use a double layer circuit board that makes repair twice as difficult, especially if a component you need to access is on the bottom board sandwiched between the two. It takes a lot of expertise and specialized equipment just to successfully separate and rejoin those two boards, let alone do any significant repairs on them.
Unless you have specifically identified the component AND it's accessible on the top circuit board, I personally wouldn't even consider attempting that kind of repair. In general, board level repairs require skills in microsoldering, meaning you need a hot air station, a microscope and lots of experience.
So if you're an electronics technician with significant experience in cell phone board level repair, then go for it. But for the rest of us average human beans, those are repairs best left to the professional.
To be honest, from your description it doesn't really sound like the repair shop actually pinpointed the issue; to me that comes across as a vague diagnosis that I suspect isn't backed up by any actual troubleshooting; they just came to the conclusion that "It's the motherboard" and gave you that generic explanation. There are diode mode tests you can do to try and figure out where the problem may originate that could help but in the end you're still in the same situation of probably not being able to do the actual repair required, but that does depend on your expertise. I've been working on circuit boards for 30 years and consider myself fairly skilled but even I wouldn't try that one.
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