Here are some tweaks my constructed community and I have implemented in a few games to make Epic run more smoothly as a competitive constructed game. We think it's pretty well balanced for draft and whatnot, so these aren't used there.
1. First player draws a card. Sometimes this is abusable if the first player simply draws and passes (you'll see why if you just start doing it) but only if they happen to have a ridiculous hand already. Lack of this meant the second player has all the advantage. Playing gold later is better and drawing is good. Player 1 by contrast can only get extra field development, but only if they don't get responded to, and see the earlier point about playing later!
2. No life loss for early mulligan. In over 90 games, it has not made any appreciable difference to winning. Sometimes it decides a game, but usually in those cases it meant the player was doomed anyway since they had a worse hand. I understand why this was implemented (to stop players from exploiting card quality) but it's not making a difference in our group, and just causing grief.
3. 15 card side deck. This is for our tournament play. Just lets us pack a few answers. The side decking is done completely blind to the opponent, so you won't know what was put in.
These have been working tremendously for us. We have some MTG PTQ toppers, Yugioh tops, Vanguard, etc in our group so these were done with careful consideration. I'm curious as to why White Wizard went with the decisions they did, though. Maybe they have some hidden wisdom we've yet to grasp.
1. Totally disagree. Your way has the first player having all the advantage. There would never be a reason to go second. Going first is an advantage in and of itself because you can establish a threat on the board. If your opponent has to spend a turn getting rid of it, you will continually be ahead on tempo. At least the way it is gives a reasonable chance you might choose to go first, even if you think choosing second is "generally" better. Your way makes it no choice at all.
2. It's possible you are correct. But compared to many other games, the mulligan rules are already pretty generous. I do at least agree with you on the principle that you shouldn't let the loss of life be a deterrent to how many cards you mulligan. It's a very minor penalty.
3. It does technically add more strategy, but it also adds a lot more analysis paralysis and time. I'm fairly certain WW isn't interested in adding even MORE time to tournament rounds, which have already been increased and yet still have many that go to time.
Total unplayed games in my collection: 7
2. Even though I appreciate the simplicity of Epic's mulligan rules, I've never been fully satisfied.
60-card constructed is rather unreliable and requires decks to be pretty flexible to win. It's difficult to build your deck around particular combos when you're at the mercy of the draw.
I'd prefer to see an option which allows for multiple mulligans, something to help that creative player actually compete, but I don't really mind the health penalty.
I haven't done any playtesting myself, but it'd be interesting to see some variation of…
1st mulligan: lose set amount of health (maybe 2 health?)
2nd mulligan: lose an additional greater set amount of health (maybe 3 health?)
3rd mulligan: lose an additional even greater set amount of health that you'll probably regret (maybe 4 health?)
3. I agree. Epic should have sideboard options for competitive play.