The more nodes in which your engine can find the best move, also if the differences appear small, the better it will play positionally and that wins games, even for someone who is as strong as Morphy. But alpha beta (maybe even more the case for PVS) is geared very much to playing 'not losing' if it does not really understand the position. It will extend the PV as far as it can and if it sees no loss, it thinks it is at least safe for now and then it will check the other moves to see if there maybe some good tactical shot it missed. To be safe, it extends those as far as possible again checking at least if in any line, the opponent appears to have one refutation to most of your moves. If anything goes wrong in this process, you have a tree which is deep, but very sparse. In all the Cut nodes there was only one move, but it proved a wrong one. To build up a new tree can literally take ages because it was ordered the wrong way. You lose on time
To remedy this a bit, you have to know more about all the other moves, before they become necessary. If you have no move yet or you lost it when putting new things in hash, you do IID. If you have at least one likely move, but nothing more, you do preemptive IID. In PV nodes, you test all moves (unless you there also just want something good enough, but that is not the philosophy of alpha beta. In other ALL nodes, you also test most of the moves. So, the Stockfish singular extension is mostly this preemptive IID, and for PV nodes I think you could try some other things because there preemptive IID is not so necessary.
The original singular extension was for Deep Blue, which did not even have a hash table. It was mostly finding tactical shots because of its very deep searches with it. But it has not so much to do with the modern versions of same name...