I've been thinking about this topic and I don't think it's necessarily a UK problem and I have a different spin on it that I've not seen discussed anywhere else.
What is the number of foreign BAME coaches across the main footballing nations? If that's where we're picking the top top talent for the cream EPL jobs (and some championship too) and BAME are under-represented in those positions, then it throws a different light on it. To select someone because of their colour is as bad as not selecting someone because of it (imo) and if we're selecting coaches from Barca, Real Madrid, Bayern etc not to mention the large influx of Italian managers and coaches, then that already fills a lot of the gaps. Young English coaches therefore whether black, white, brown or yellow will have less openings available without dropping down the leagues as Sol has now done. I do get the Gerrard argument and the Lampard one, but also Viera and Henry have been given great opportunities without doing any more than they have for the same reason of them being recently retired top players who have good contacts and good networks. I'm sure Derby or Rangers would have been happy to have taken either of those two.
This of course isn't to say that BAME coaches aren't under represented or that there is no racism in the game or even that Sol has been treated fairly, as I don't know any of those things just a different take on the reasons why.