An objectionable acquaintanceship may be reconcilable.

The person leaving might not be objective in a situation and might realize that they miss the metaphorical bridge.

A person you dislike might be a valuable resource in other ways beyond social (especially in the referenced example of a medical professional).

Things change. For example:

• burn a bridge at a company w/ a terrible boss - boss leaves and is replaced by a much better manager, but you have no shot because HR is still pissed at you
• burn a bridge w/ a date - you end up working with that date and they remember how rude you were and end up making things suck for you
• burn a bridge w/ a doctor - doctors tend to be friends w/ other doctors, so other doctors may choose to not bring you on

That doesn't mean you should let people walk all over you, it just means a little professionalism goes a long way. If you can't stand your boss, give them a reasonable notice that you're leaving. If your date is late, send them a text saying something came up and can no longer wait for them. If your doctor sucks, thank them for their time and ask for a referral for a second opinion, or if they take too long to see you, tell the front staff to cancel your appointment on your way out.

You don't have to put up with nonsense, but you should handle it as gracefully as you can, because it doesn't cost you much and you never know if it'll end up mattering.

Because it's a small world. You could very well have to interact with former colleagues again or have your behavior shared with others.