Generally I couldn't care less about whether a player is British or not and a lot of the people who do often do so for reasons that are rather reductive in thinking.
However, there are certainly some definite benefits. A young British player will usually have fewer problems adjusting to living Manchester, is probably less likely to want to leave the club for foreign lands at some point in the future and brings something in terms of marketability given the national team is a product. So a British core can bring a sense of stability, I guess.
In terms of money it's a double-edged sword. Buy them early and relatively cheap (as we did with James and as we may do with Longstaff, or as Liverpool did with someone like Robertson) and the fact that they're British will protect their market value to a certain degree, even if they fail here. Not to mention massively inflate their value if they're a success. However if you buy them on the wrong side of building hype (as we are with Maguire, if that happens) and you pay the British tax instead.
My main issue with this idea of returning to a British core is that we already have a fair few British players. Shaw, Young, Smalling, Jones, McTominay, Lingard and Rashford all knocking about in or around the first team. Our problem is quality, not nationality.