I've encountered my first case of "that player".

I wouldn't ever tell anyone flat out that their idea is stupid. I'm sure it was stupid, but if you say that it makes people defensive and unwilling to share things with you in the future.

First, stick to the PHB+1 rule and don't let him wheedle out extra benefits to his character. There are hundreds of character combinations with the PHB+1 rule so if he can't find something there he wants to play then he's not looking hard enough. If you want to expand beyond PHB+1, that's fine, but set some rules so you don't have a player show up with a homebrewed Lizard Elf Nighthawk whose sole purpose is to be just broken enough that he doesn't draw the DM's ire.

Second, have a conversation with him that D&D is a cooperative game and by doing things like adding unnecessary randomness to his character's spells would be fun for him, it would not be fun for anyone else. Tell him you and the rest of the players would love to have him play, but if he's not going to engage in the cooperation aspect of D&D, then maybe this isn't the game for him. Some players just want to see the game in chaos and trust me, it's better to get them out than try and rein them in. It will only end up destroying your campaign.

Tell him no. Easy.

It's a lesson we probably all learn, but I'd highly recommend next campaign having a Session 0 where you lay out specifically what races and classes are allowed, and what if any house rules are being used. Otherwise, default to Rule 0 - The DM is the final arbiter of all things in the game.

Having said that, The Wild-Magic Sorcerer is one of the worst-designed classes in 5e. There are a few simple home rules that you could use to make it better.

For one, any class ability that relies on the DM remembering to do something instead of the player remembering to do something, is bad design, IMO. So with the wild-magic sorcerer, the DM has to remember to tell the player to roll on the Wild Magic Table in order to refresh the Tides of Chaos ability. New DMs, and DMs who have a lot of other things to track and keep in mind, will often forget to do this, taking away a core ability from the class.

So I houserule it that the player, after using their Tides of Chaos, can simply choose to roll on the Wild Magic Table any time they cast another spell in order to refresh it. That way the DM doesn't have to worry about it. Or, just have their Wild Magic roll number go up to 10 instead of 1 after they use Tides of Chaos. Once they trigger wild magic, it goes back to 1, until the next time they use Tides of Chaos, then back to 10. etc.

This way, the work and job of remembering to do this is all on the player instead of the DM.

I'd tell him to cool it with the homebrew. Tell him that you can approve or deny his options for wild magic, but don't spend your whole like iterating and providing him feedback. You've got more in your session to prepare for than that.

This belongs in the problem player megathread.

"I've got enough work to do as DM. I don't want to also have to keep deciding whether your homemade rule-of-the-week is acceptable or not. Stick to book-legal builds."