I think the etiquette on SE is to first comment on the comment and suggest that (one of) the commenter(s) convert/expand their comment to an answer. If they don't react (say, within a week), that'd be carte blanche to do it yourself. In this case, I'd say referring to the comments ("As @x wrote in their comment, the answer is...") is sufficient; if you want to go beyond, you can add a link to the relevant comments -- you can get the target from the time stamp (in light gray) next to the comment -- like so!
I don't see why there should be any requirement on who can do that. (In fact, it might be a good way for new contributors to get started on gaining reputation!) If you feel unsure, you can always mark the answer as a community post; this may be appropriate if you're just literally copy&pasting comments,1 but if you're also expanding on them (adding explanations, literature references, examples), I'd say you deserve any points the answer gets you.
However, I'd temper my expectations on increasing the answered question percentage -- old questions are often essentially abandoned, and receiving an answer this late won't necessarily mean that it will be accepted. (I assume this will be the main reason why people are less motivated in answering old questions.)
 But be aware that if someone considers comment copying "reputation stealing", they wouldn't be mollified by a community post since you still deprive the comment author of the chance to get reputation -- even if you don't get any either. But this is a non-issue if you give the commenters time to write their own answer first.