Short answer: yes, you can paint a street bench, and it does not have to ruin the finish. What usually ruins the finish is painting straight over dirt, peeling clearcoat, loose rust, or slick powder coating without prepping the surface first. Paint itself is not the enemy. Bad prep and the wrong paint are.
Before you do anything, check if the bench is public property. If it is a city street bench, get permission first because it may be maintained by a local crew. If it is your own outdoor bench, painting it is usually an improvement rather than a disaster.
For a metal bench, clean it thoroughly with a degreaser, rinse it, and let it dry completely. Lightly sand the old finish with medium-grit paper or a sanding sponge so the primer can grip. Wipe off the dust, then apply a rust-inhibiting exterior primer. After that, use a weatherproof paint made for metal, such as spray enamel or brush-on exterior enamel. Thin coats work much better than one heavy coat.
For a wooden bench, scrape and sand any flaking or grayed areas until the loose material is gone. You do not need to strip every bit of old finish if it is still solid. Use an exterior primer or a paint-and-primer combo rated for outdoor use, then apply exterior paint or solid stain.
If you want to repaint a street bench so the new finish lasts, wait for a dry, mild day. Let the final coat cure for at least 24 to 48 hours before heavy use. That patience is what separates a durable outdoor bench finish from a paint job that starts peeling in a month.