I've attended a few UK vote counts. Pencil is also used - but you can bring your own pen if you'd like.

I think it's mainly to prevent smudges as the paper is folded to be put into the ballot box. Pencils are also more reliable than pens, and have a longer shelf life between votes, I'd imagine?

At the polling stations & counts I've been to and overseen there is pretty much zero opportunity (or interest) in changing people's votes on the papers. I'd imagine this is the same in most first-world countries. In fact, once I spotted and got corrected a paper missed for a candidate opposing the candidate I was a counting agent for.