Well,I think the "removing useful information" bit contradicts with utility to being with.
As in, if you are a utilitarian, useful information == helps maximize utility. Thus the trade-off is not possible.
I can think of some contrived examples where the trade-off is possible (e.g. where the information is harmful now but will be useful later), but in that case it's so easy to "hide" information in the modern age, instead of destroying it entirely, that the problem seem too theoretical to me.
But at the end of the day, assuming you reached a contrived enough situation where the information must either be destroyed (or where hiding it devoid other people of the ability to discover further useful information), I think the utilitarian perspective has nothing fundamental against destroying it. However, no matter how hard I try, I can't really think of a very relevant example where this could be the case.