The damning part is that even if the repair place uses an actual Apple battery with all the circuitry exactly the same the phone treats it as a complete unknown because it hasn't been approved by Apple and authenticated. If I open up two identical iPhones and swap the batteries I shouldn't have diminished functionality, the phone should still fully report everything it knows about the battery health.
What if Apple's installer screws the same thing up? And if that was really a huge issue just locking out any battery monitoring is... worse because now there's just the meaningless 'You're battery isn't Apple approved and installed' warning.