I was in a band where the lead vocalist (lady) and drummer (dude) were a couple. Somehow they made it work, but they probably had to work twice as hard to make it work. They often had to pretend they were cousins or something, especially at shows where fans would approach the singer and she had to pretend to be unattached otherwise it might turn off fans. Maintaining stage image vs real image. I believe they were a couple before even starting the band. So that might have an effect on dynamics as well.
And, as others have said, couple drama sometimes snakes its way into the band and it becomes family drama like when the parents' fighting affects the kids like secondhand smoke.
There is also the risk of a power imbalance within the band when two members of said band are dating.
Some say it's sorta like when you date someone from the same workplace. Like, what if something goes amiss in the relationship? You still gotta work your day job with them every day.
But on the other hand, there all sorts of risks when dating anyone. You might love your partner but can't stand their friends. There might be disapproving family members trying to sabotage things because they don't approve of your life choice.
No matter what, relationships are hard work. Some relationship dynamics are more complicated than others.