By rule, if there is no official's timeout the player does not have to sit out a play and can return immediately.
Do yourselves a favor and call timeout for blood, injury, helmet off, or improper equipment. It's all covered by the rules. I've seen situations where the TO was not called and after substitution the offense had to hurry to avoid a delay of game, or the offense was held up so a defensive player could be brought on. Don't make the situation worse, call the TO.
Remember that end of either half is the only thing that "buys" a player back onto the field.
First off, I 100% agree with what you wrote. However, I wonder about a potential rule/change/adjustment, which I'm acknowledging is "as seen on TV".
Runner dives up the middle, linebacker dives in, stuffs the charge but the runner's helmet comes off in the contact. Nothing illegal, just the helmet comes off. The player knows immediately he has to sit out a play, picks up his helmet and immediately runs off the field. We kill the clock for the helmet, send him off, which takes 5 seconds and restart the clocks. By rule, the play clock is now 25 seconds instead of 40. However, since the player leaving took minimal time, the offense now has less time to run the next play. They should have 35 seconds left, but instead they have 25 on the restart.
How many people would be in favor of being able to pause/restart the 40 second clock for such an infraction? I get that it's kind of an additional penalty on the offense for having the helmet come off, but do we need that? If anything we'd be incentivizing the player to drag his feet getting off the field to allow his team additional time to call a play/substitute etc.
Alternatively (or in addition), the play clock can be reset to 25 if the officials feel the player is trying to draw it out. I feel this is where it all falls apart because we'd need good play clock operators who are paying attention and know the rules or can follow directions at least.
This would also not apply to a defensive helmet since the clock resets to 40 in that situation.