It's not just the young players though. At the moment any player from a EU country automatically qualifies to play in the Premier. Going forward from Brexit (unless they negotiate special terms for EU players), all players will need to meet the strict work permit requirements. As an example, Dimitri Payet would have failed the criteria when West Ham purchased him and would have had to gone to appeal. Plus it does away through all these South American players qualifying through their dodgy Spanish and Italian passports.
There is a potential down side of Brexit to Everton's own academy. The likes of RS, City, Chelsea and Arsenal bring in a lot of youth players from Europe, so presumably there will be more competition for young English lads.