I wouldn't worry with it.
I also wouldn't pay much heed to the theory that "not having proper power supplied to the starter by the factory wiring will damage it".
Just so that you understand where I'm coming from - yes - one of the easiest ways to damage an electric motor is to supply it with a lower than normal voltage - but - that is more applicable to a motor that runs continuously, that one that is used intermittently as in the case of a starter motor - and - the lower than normal voltage would be the main supply that is fed through the heavy black cable, not the solenoid control lead.
You can also, at least theoretically, overheat and damage the solenoid if the voltage supplied to it is too low - and this is where that clicky fix relay can make a difference - but again, under normal circumstances you wouldn't have the key turned to the start position long enough to overheat the coil windings.
If you've ever taken the time to read your owner's manual (any vehicle owner's manual), you will see several warnings not to crank the engine for more than 15~30 seconds at a time, and to allow it time to cool in between cranking.
So - when you turn that key and it goes "CLICK" what are you going to do, hold the key down & pray - or - release it and try again? After repeated attempts there will be some heat buildup, but you should at some point realise that it's not going to crank, and I believe for most of us, that point will be before any damage is done.