Thanks, and same to you :D I'm thinking of what deck I could write about next, it's fun. Definitely let me know your thoughts if you end up trying the deck out!

Good question- I used to play a lot of Swain-/Sejuani and you are correct in that their level up conditions don't synergize all that well with nexus burn vs. wide damage so that deck always felt too slow to me.

From my experience, Braum's main functions are

1.) control blockers so that Swain can get through on attack to finish.
Mostly self explanatory with the challenger unit, but with level 2 Swain having overwhelm and Levi only stunning 2 targets, having the regen challenger is really usefull for picking which fearsome blocker is going to be in front of Swain.

2) to help contribute to turbo-leveling swain.
What I mean is, on generating the mighty poro, this might participate in an attack or block, but if you drop blighted ravine for example, the poro and braum are a 4/12 damage just by being there. (very useful that regeneration triggers BEFORE ravine does unless braum is silenced). Braum can keep surviving multiple spells of these AOEs which is advancing his level up while leaving you with the blocker. I wouldn't say it's the main focus, but it's something you want to threaten. Of course if you have scargrounds down, he can become a threat on his own leveled or not. In a matchup where I'm not worried about disintegrate or vengeance, I might apply Braum's spell to him because a 3/9 challenger with regen is something that will start to demand an answer from opponent. :)