Foreign Teams In English Trophies As Guests

How about this?
The Scottish allow Northern Irish, and Welsh sides in the Scottish Challenge Cup.
So my idea is why don't the English allow guest teams in their cup trophies.
For instance all Scottish Premiership sides not in Europe, plus selected Welsh Premier sides, and perhaps Belgian, French and Dutch lower tier sides in the Football League Trophy?
Or perhaps all Welsh Premier, Scottish Championship, and lower tier French and Dutch sides in the English non league FA Trophy?