They do in the UK: you can bring a pen if you want, but you should probably make sure it's something which quick drying ink so it's not likely to mark other parts of the ballot when its folded. In terms of tampering with the ballots it really doesn't make much difference: there are ways which are far easier to pull off and harder to detect to tamper with them than erasing pencil marks, and the way the election system is designed to protect against those ways also effectively prevents any issue with what was used to mark the ballots.

They do, in the UK. Supposedly this is due to the possibility of pens containing disappearing ink. More likely this is to avoid ink being accidentally smeared across the ballot, since it has to be folded.

Why?

Presumably because a ballot filled out in pencil is not immutable — the pencil marks could be erased!

That's why the sealed ballot boxes are accompanied by by two officers and the candidates are all present at the count.

If you tampered with the ballot it would only be discarded due to the rubber marking in the "wrong" box

I don't know about the UK, but in Australia it's attended by the candidates' representatives, called "scrutineers". The counting is done at the polling place, so the candidates can't be multiple places at once.

I've scrutineered before, and it all seemed to work well.

https://en.m.wikipedia.org/wiki/Scrutineer