Did Rema have a copy of the Maharil?
If yes, isn’t it odd that he would get that so wrong?
When the Rema says you can haircut on Friday for k’vod shabbos, if that were the only reason,then you would be able to haircut every Shabbos during Sefira – L’kvod Shabbos. And if it was because haircutting on Sunday is Bizayon Shabbos, then it should be Assur all year long. So the Rema‘s reasoning of K’vod Shabbos must be like the Maharil, and is coupled with the fact that you were unable to shave on Lag-B’omer Sunday since the Christians forbade it, and therefore you can shave on the Friday before, L’kvod Shabbos not to force a Minhag on people more than the bare minimum, as @sam2 said.
And why didn’t the Rema just say you can’t shave on lag b’omer either when it falls on Sunday? What mitzva is there to davka shave on lag b’omer?
@simcha613 forgot to mention, that the Rema holds that the Talmidim of Rabi Akiva died from Rosh Chodesh to Shavuos excluding all the days of Rosh Chodesh, Lag Baomer, and 3 days of Hagbala . You add them up they come to 33 days (i probably missed a day or 2) but the idea is that according to everyone, no one died on Lag Baomer, so even if you shaved on Friday you can do it again Sunday. this should answer all ur qs.
So, R’ Schachter says, nowadays there is no reason to permit haircuts on Sundays.
I’m sure R’ Shachter was refering to the Mishna B’rura and what we call ‘the first half and second half of Sefira, and not the Rema’s Shita per se, because no one holds of this Rema nowadays.
(I assume he is unaware that some states still have these laws and it’s possible that if you live in such a state that you could get a haircut on Friday)
I doubt that would be the case with Sunday closing laws, because you can always shave or take a haircut yourself.