Hi and welcome to the forum.
It’s to stop fraud and theft. Anyone could steal or buy a stolen phone etc.
Other companies may not be so conscientious as they just want your money not your integrity 
If you contact the seller maybe they can provide a copy of a bill of receipt etc.
You probably don’t have a valid warranty once you’ve taken it apart without advice from Fairphone.
Regarding a DIY repair. You cannot user exchange the core module so the only option given your suspicions is to replace the display module which you can do yourself for a smaller financial outlay.
You don’t say what is wrong and what you have done, in detail to effect a repair. Maybe someone here can provide some insight and if you are lucky you may find a fairphoneangel near you.
The connector
- Are the pogo pins movable
- Are they and the display contacts really clean
- Are the five ‘solder’ contacts with the core module shield clean
- When you re-fasten ensure you do the screws around the contacts first, not too tight, then the remainder ~ not too tight , then tighten the ones around the contacts etc.
See this post and those below it