Controllers are often not aware of what reserves are required on a sector or approach level, it's their job to separate aircraft, end of story.
True but reserves are easily worked out on a time basis so the average controller would have some idea.
That said I know of a few stories where ATC could perhaps been a little more aware of reserves and in one case because of lack of knowledge almost contributed to a serious 747 incident at Brisbane. I was heading south to BNE (overflying) and on approach listening to the whole saga unfolding. East-West F28 nose wheel collapsed on runway - no action from ATC for a good 20 minutes (BNE was much quieter then). ATC no action to remove ac, no advice to crew until on their frequency and then told to hold (at low level). Back then 747 operator had dispensation from variable reserve, weather was CAVOK no holding requirements, was out of SYD to BNE and then onto Japan I believe - so basically very low on fuel into BNE. No chance of getting to an alternate, Captain getting a bit testy as you might imagine, demanding landing time with response from controller "we understand your situation sir" and so on. Crew eventually declared an emergency with no reserves and no options. ATC / Ground staff responded at that point and cleared the runway - dragged the F28 off.
In another case a friend was in a Bandit - destination was forecast TEMPO and he carried appropriate holding fuel. He did 2 approaches and did not get in. At that point he elected to hold because not enough fuel to get to an alternate. ATC assumed operational control and directed him to another airport that was, say 40 minutes away, he very wisely declined the directive and of course there was a report and a lot of paperwork but the point ATC neglected to take into account that 60 minutes at holding rate is less fuel than 40 minutes at cruise rate so despite the fact they had the fuel figures in front of them they did not interpret them correctly.
To be fair the two incidents above occurred a couple of decades back and things are a lot different now. But I think whether it is their job or not that knowledge is worth having because there may well be times where it comes in very handy.