Load of bollocks, as always. Your "you just wont a fashnuble forrin" is the more clichéd schtick at this point than actually just wanting the fashionable foreign manager would be.
Amorim is a popular choice because his teams have played good football, he's turned around clubs who were in the doldrums and he seems quite likeable.
Southgate is unpopular because he had a stacked England squad playing terrible football and underachieving whilst doing so.
Nobody would have any issue with an English manager who was actually good.