Nope I don't. I think a better idea would be for English players to not move to clubs if they aren't going to play. The recent moves to Germany of a couple of high profile youngsters is a good start, as is the likes of this England squad which has started to have a mix of players who came through other clubs rather than sat at the big ones. Pickford, Butland, Walker, Rose, Maguire, Trippier, Cahill, Alli, Vardy, for example.
I'd suggest it's minimal impact, and if all lower league sides were drawn at home it would negate most of that and probably benefit more than those that lose.
As it is, it really is a small number of smaller clubs who would first need get a reply away to a Premiership side in order to miss out.
By recent reports I'm assuming you mean the one in the last week or so, and was based on our players in this particular squad. I'd suggest if you don't look at England players but players playing in England that would alter the results, and that's what we're talking here. Too many games without a break in the English season. Rashford, Welbeck, Loftus-Cheek, Henderson, Delph, Jones, Cahill, Stones, and Rose have had reasonable breaks this season where they haven't played due to injury or not being fancied which would have skewed that report.
Not sure if this is a point I've made? The season has got slightly longer over the passed few years, as I remember the FA Cup final was a week earlier in 2001 but there are midweeks where some teams do skip fixtures, and better spaced games with this break would seem to make more sense .