Are there any reasons why it would be bad for me to have a question Closed (rep loss, less likely to get good answers in the future, ...)?
Having a question closed does not impact your reputation at all.
It's unlikely that having a single question closed will make it more difficult to get answers in the future. On many sites, no one will particularly notice. Having a bunch of questions closed might get you labeled a crank, but one question is unlikely to draw notice. You might get a better answer from the meta of the site where you posted, as I don't know what the community is like (even if you told me what site, I might not know).
The next step after closure is a delete vote. This won't automatically delete the question, but it might.
There is also no general penalty for having a question deleted, but having a question deleted will reverse your reputation changes from that question. If you currently gain reputation from the question, you will lose it if deleted. Note that the question does not need to have a positive score to give you reputation. Upvotes give more than downvotes take away, so you may gain reputation from a question with a negative score.
If you have no answers and negative reputation from the question, you may want to delete it yourself. That will save the community from a delete vote and will give your reputation back immediately. You don't have to do this though. If you're satisfied with the current state of the world, it's fine to let things go.
If you currently have positive reputation from the question, you may want to try to salvage it. Editing a question to make it more narrow is perfectly legitimate and will kick off a reopen vote. Or you can do nothing and let it go. You won't lose any reputation but what you gained from that question.
A lot of this calculation depends on the specific question. Is it easy to salvage? Is it likely to be controversial even if changed? How much do you need the answer?
I wouldn't get too caught up in altruistic reasons to salvage the question. Is the question useful to you? If so, you might want to try to salvage it. If it's not that useful to you, then it's probably not that useful to others. If it is useful to someone else, let that person ask it. Note that salvaging a "Too Broad" question will tend to make it less useful to others, as the focus will narrow to cover less of the subject.
Stack Exchange tends to work best when questions are driven by need. If you need an answer, then it's likely that someone else will as well. If you don't, then perhaps no one does. If someone else does, let that person ask. That way, the question will better reflect what that person needs.