Quite correct, not all aircraft systems have flyback protection. This aircraft does and it seems its not working , or at best doesnt behave correctly when its connected. In general though its good practice to clean the electrical system of unwanted electrical noise.
Voltage spikes from the solenoid can destroy sensitive devices , and many such devices exist in our aircraft from voltage regulators to intercomms and radios, a big list of things.
Setting aside the technical question, if as a maintainer or a pilot you get a feeling that somthing is just not quite right eg that little flick of a gauge that you have never seen before and it does it again or more often. You gotta at least consider is it a developing fault . Do not ignore the early signs your life depends on it!
So i guess chasing a diode issue that may not be completly essential to operating the AC might be thought of as time wasting, its not , in this case i think we will find that the diode was never originally wired correctly and when it failed it engaged the starter solenoid. That is what we are sorting out as to why a replacement diode is not operating in the same way as the old one did.
Here is a guess ( no facts yet to suppoert it ) original diode was wired across the switch in reverse, when it should have been across the coil terminals . the back emf from the starter coil eventually zapped it thus engaging the coil full time and starter motor runs. Remove the old diode and all ok. Fitt a new diode but due to inexperience with diodes , its fitted the wrong way round , coil current is carried through the diode and damages the diode, which in turn pulls in the solenoid and runs the motor. We are back to where we started ( no pun intended lol) But lets see what further investigation turns up without facts its all a guess.