I've always painted them, don't think I have any pics atm, as I'm at work. (shhh don't tell the boss.lol) but a full black acrylic would give you the same look. I'd worry about tint in that any decent aquarium light would shine through it and show the wall behind. Also it would likely be far more expensive than just a thin sheet of black acrylic.
Think of the resale! I've gotten a few used tanks in new conditions save for the painted back. I've almost walked when I saw them and got the price down! My 125g cost me 1/2 what I showed up to pay and he threw in a Rena xp3 I don't even use!
And I didn't fake walk away like a jerk either! I decided it was more worth it to buy new at 3x price than waste a day scraping that crap off with a razor blade and heat gun. Price drop changed my mind. But I almost regret it after the sore wrist and fingers for days.
Just use your old tape on background and spraypaint that. I did couple times. Allows me to change em up.