Do payments to relegated teams widen the gap between promoted teams and non-promoted teams?
There's a huge gap between a team not promoted and one promoted and then demoted the next year.
From the info I could pull, championship sides receive £2.3M each from solidarity payments. A club relegated from the PL receives £24M in their first year down, £19.3M in their second and £9.6 in their 3rd and 4th.
Everything is going to be shuffled with the new (and larger) TV deal taking over, but it seems like the rough ratios are going to stay the same. PL teams get a 100% share, relegated teams get 55% year 1, 45% year two, and 20% year three with the year three payment only being sent if the team was in the PL for more than a single season. Championship sides receive a 30% share of the 20% parachute payment (which seems to be a 6% overall share) for being in the Championship.
So the difference between a team that spends 4 years in the Championship and one that gets promoted, spends a single PL season, then gets demoted forever is very significant. Even excluding the revenue earned while in the single PL season, you're still talking £60+M
The revenue sharing and parachute payments are a double edged sword that way. On one hand they help a team like Villa not have to suddenly sell all of their players to avoid bankruptcy, but on the other hand they seem to be likely to create a class of tweener teams. Teams that make the PL once every 2-3 years and rely on that revenue to maintain spending well above what a mid table Championship team can handle.
What if every team played as hard as they do? It would be amazing. It's cool to see the Manchester teams fighting each other for CL/Europa. Who will win? Between Leicester, Spurs, Arsenal, and a Manchester team, who will do the best in the CL? The Blues are 12-12-12. 
