It’s taboo because in practice, such relationships aren’t actually consenting, in the “no strings attached” sense.

Keep in mind the potential problem isn’t just between the supervisor and the subordinate, but with the supervisor and their entire department. Because it’s natural to suspect the supervisor’s lover of getting preferential treatment in terms of pay/benefits/promotions. This suspicion tends to cause an unhealthy work environment.

"The supervisor already, necessarily has a lot of power they could potentially abuse. So let's put some rules in place to check some of those potential abuses, and give us clear-and-fast reasons to discipline if needed."

It's extremely poor judgment to date some that reports through you. "Power corrupts"-type stories are everywhere. Don't trust yourself to be the perfect exception; have some self-control.

Or, if you must, move to a different role or job! You're the one in the scenario with more options. And remember: most relationships end! Then it gets even messier if you work together directly, especially if they report to you. You break up, you can't work together well, now what happens? IME, nothing good for the person in the management role.

An employee in a relationship with the supervisor getting a promotion, objectively deserved or not, has the appearance of bias and favoritism. A supervisor having to make layoffs and keeping their spouse around is another such example.

Because it's not just impropriety, it's the appearance of impropriety. It erodes trust in the organization to treat employees fairly by their competence/skillset/behavior/etc.

Even if the supervisor isn't abusing their power, it can still be an issue. It can lead to people thinking "Is there going to be come back if I break up with this person?".