It's a possibility, another might be the return spring on the gears. The wishbone shaped spring works to engage the gears, The coil spring helps disengage the gears. With the spring out, stretch it a bit. This will not so much make it stronger but push the gear farther. As springs age they get weaker, this is evidenced by measuring the over all height of the spring. If they measure up a bit short you can shim them, like done with valve springs or on a lot of less critical springs, stretch them.
On my 75 that had starter issues I not only tightened the wish bone spring, I tightened the return spring.
The safety relay is the relay you are talking about. It was first used in 72 to protect the starter system by turning off the power to the starter relay when the alternator created about 4.5 volts on the yellow wire, this tripped and held the relay. This stops the starter as the engine starts, it also prevents the starter from working while the engine is running. In 78 they added a second half to the relay that would turn on the headlight. Up to 77 the safety relay had 4 wires and just controlled the starter. 78-79 had 5 wires, 80 up had six wires, these controlled the lights also.
As I've said before the safety relay is much faster than your thumb. By the time you realize the engine ha started and you release the button, the has already been over run for a bit. The safety relay prevents this.
I doubt it will ever hurt the starter itself, but it can damage the gears and the cross shaft the starter uses to engage the engine.
It's not hard to wire in a safety relay. You can even use a lighting relay. I have picked up such relays at the auto salvage yard. They don't charge much. Get the 5 terminal ones. The 4 terminal ones just turn on a circuit, the 5 terminals ones turn a circuit off.
The terminals are numbers. most show the internal wiring on the side. The power wire too the starter relay cut it and hook one side to terminal 30, the other to 87A. These terminals are on when no power is applied to the relay.
No hook the yellow wire from the alternator to terminal 85, hook terminal 86 to ground. Now as the alternator starts to produce power , it sends power to the relay, relay trips and cuts power to the start relay.
Is using a stock relay, most any stock wiring diagram shows how.
Leo