You don't have to like them to learn to live with them. After folding ours up and securing it to the backstays for the first few passages, we left it up virtually all the time. I say "virtually" because I don't remember ever taking it down, but we might have.I'm with you on Biminis. I don't have one (mainly because there's no room under the boom), but I've sailed on boats that have them and I find them very claustrophobic. From the sin cancer standpoint, I totally understand, but I still don't like them.
We had a heavy-duty bimini that was specifically designed for sailing, rather than sitting on anchor. It was strongly built, heavily reinforced, and secured to the boat in multiple places
When passagemaking, you generally aren't obsessed with sail trim every second like you are when racing, so the fact that it may be slightly more difficult to check the sails is less critical, as long as you still know when to reef and can monitor chafe.
Sitting out in the sun for days on end without some sort of cover gets old very quickly, especially when you are older. For us, the answer was a sailing bimini.
The dodger provided similar protection when you were sitting in the companionway, but the weather had to be good enough to leave the drop boards out for that to be really useful.
We did not have a cockpit enclosure. I draw the line at those.
But when it comes to biminis. handsome is as handsome does.