Major sports are dealing with at least 3 time zones...hard to make it a perfect fit for them all.
When I lived in Hawaii, Sunday NFL games started at 7:00am, and MNF started at 2:00pm and was over before I got home from work...
starting at 7 PM eastern gets the game over by 11 or so, and on the west coast, it gets the 2nd half of the game in between 6 & 8. If a game is a blow out, perhaps they don't watch on the west coast, but that's perfect after work bar watching and easy for kids to watch. This really seems obvious. The current set up, starting at 8:20 on the east, discourages kids and even adults from starting to watch games if they know they will not be up at the finish. On top of that, if you are going to cater to a coast, cater to the more populous side of the country. Vast bulk of teams are in the Eastern and Central time zones so it also works better for most of the fan bases (off the top of my head, only about 8 teams are mountain or pacific - SD, LAD, LAA, SF, OAK, SEA, COL, and AZ).