1. What do you have to "carry"? I don't know how well you understand the game, but you don't need UDK in the least at this moment. For the next several months, the content you'll be grinding can be completed wth farmable champs. UDK's claim to fame is shutting down Rotos and Head of Mischief......you don't have to worry about that for a while.
2. At your stage, you will be struggling for speed, and Khatun is one of the best there is for f2p players. You calling HK a "D-tier garbo champ" reeks of entitlement. I have clanmates who still use her, and they are ages ahead of you, so chill out with the whale attitude. Not to mention, she can fit into every team, from Clanboss to Campaign to Arena.
3. There will be more. Like somebody mentioned, it takes a while before you get the first legendary, unless you are very lucky. So curb your expectations about champions and stick around until the next leggo. Also, start keeping a mercy counter and save shards, if getting good champions means so much to you.
I'm genuinely curious where you got the idea that Khatun is a garbage champ. I don't know a single content creator who would rate her as D-tier. We're talking about a turn-based game, turn meter and speed are kind of a big deal. Imagine playing a game of chess, but you're allowed to make more moves than your opponent....it's that kind of important.