The sphincter is a muscle. Like any it can be stretched and if properly done so with appropriate warm-up can be done so without injury. The reference to force in the OP is key. If you force it open as opposed to gradually stretching, you risk injury and therefore damage. Many kinksters train their bottoms to accept plugs dildos, fists etc and then after play (sometimes minutes, but can be hours, or a day at the outside) and cleanup it shrinks back down to normal and seals just fine.
From experience, yes using plugs does fix mild hemorrhoids, I think by stretching out the muscle fibres and allowing trapped vessels to pop back in, and then settle back in place in a controlled fashion as you remove the plug. A hot washer helps. I think it happens in the first place by pressure forcing blood vessels out between the muscles then trapping blood there which can't release so you get a small distended bit of vessel sticking out which is really sore and irritated.
People who play and like pain, or do so affected by drugs so they do not heed their body or deliberately damage themselves, can end up incontinent and may require surgery to repair things so their sphincter seals again. In particular it's not uncommon for gay males using ice and poppers to do extreme anal play to experience this.
Anal training involves warmup and dilation but in a sustainable fashion not intending to injure or impede function. As babykeiff says, dilation on its own won't cause incontinence. But repeated injury will.
You can use plugs and toys and not risk affecting anal function if you do it properly. Likewise you can use other methods to achieve bladder and bowel continence but it is sage advice to be careful what you wish for. Life is a long time. Consider your future self and circumstances, not just the next while or your current fetish drives. (Are you listening, self? lol)
xx NC