First of, I am not saying that the RNG factor makes it unfun. That's what this gamemode is about after all.
When I queue with 7 other players pre and each of them tells me in the game that they are constantly on 1 Gold and I have a perfect 5 interest over the whole course of the game, have the most rerolls, have the highest streaks, have the champs that were picked the least and so on, but every single game I am the only one without a LV3 Champion and lose due to worse item drops, it's just not fun.
Add like another field next to your normal draw pool where you will get one Champ you already got (field or bench both), but it will cost double the gold. Rerolling won't refresh that field, just new rounds would. That way people that can't change too much with their lineup because they have their field and bench full because they are actually strategically good wont get thrown over by the game.
I really like the concept of having to adapt to the RNG / draw percentages, but it's just like in Dota Auto chess - with a _bit_ of luck and good amount of knowledge you can get into top 3 almost every game. You won't win a single game just because you are better, no matter how bad your enemy is. And that is the most tilting thing there can be.
Another idea would be to be able to be able to manually decrease the maximum Champ Tier you would like to get in your reroll. I tend to have two Lv2 Champs on the end of the game and even if I am the only one having this particular champ, I wouldn't roll it again, because it's Tier 1 and I almost only get 3+.