Personally I am mostly comfortable with the RNG surrounding champions because it brings freshness to every new match of TFT. I like the fact that everyone is inclined to build a comp around the champions they have available. It brings diversity to the game instead of everyone just building the most overpowered team comps, which would happen if we had the choice to just get any champions we wanted. However, I will say one thing that can get frustrating is not being able to complete a 2 or 3 star champion just because you didnt get lucky on rerolls. I've had matches where I was sitting on 50 gold and rerolling 25 times didn't get me the champion I wanted, this just felt unfair. It would be nice to have the option to pay a potentially high fee (25 for 2 star, 50 for 3 star?) to complete a champion if you are missing just one more. This would be a good feature as it would let people choose whether they want to sacrifice their high income for a strong champion or keep their income and be able to increase their team diversity (since having a high income basically means you get consistent rerolls every round)
That being said regarding champions, I am personally very unhappy with the extent of how RNG items are. Its not fair that some people can receive a bunch of items during the minion/monster rounds just because they got lucky, while others could have bad luck and not get any items. I believe a good fix for this is to either:
1. Make it so everybody receives a minimum of X>0 item drops during the minion/monster rounds. A simple and fair solution, everyone has items, and even if the items are random people just have to think better about which champion they want to give items to.
2. Increase the chance of receiving an item from a minion/monster round if no items were received in the previous round(s) and decrease this chance if you did get items. With this solution people who got an early lead wont just snowball ahead, and people who got unlucky early would have hope for coming back later in the game when they faced later rounds of monsters.