What stops you from desoldering the bad connector and soldering on a new one?
SMD rework sucks if you're not used to it.
It sucks if you are used to it!
Not in my experience.
But dense SMD connectors with heat sensitive parts and damaged boards more than just suck.
Assuming you can find the part "full board replacement" may not be as bad as it sounds for a monitor. Your main point still stands though, ideally a faulty connector shouldn't require to replace anything besides the connector itself.