We have 2000 keywords and I suspect most of them do nothing

Mostly inert, with two real costs and one genuine risk. The costs: they make every screen harder to read, and they make any bulk change dangerous because you cannot see what you are affecting. Neither shows up in a spend report, and both are why accounts like yours get worse slowly rather than suddenly. The risk you named is real, and it is why I would pause rather than remove. A keyword with no impressions in Q1 might be a Christmas term. Look at a full year, not a quarter, before deciding anything is dead - and for a six year old account, look at two. What I would actually do: pause anything with zero impressions across a full twelve months, leave everything else alone, and revisit in six months. That's an afternoon, not a week, and it is reversible.

Before you pause the zero-impression ones, check why they have no impressions. There is a difference between "nobody searches this" and "this is blocked by a negative" or "this lost every auction because the bid is far below market". The first is dead weight. The second is a bug you would be hiding rather than fixing, and I have found several of those in exactly this kind of clean-up.