I'd never thought about it too much until this thread, but I actually end up doing this quite a lot. It probably comes from my love of jank shite. My decks will usually have a certain thing in mind I want it to do, but usually that isn't specifically related to the commander. Some good examples are:
Old frame cards only. Originally I built this deck with
Cromat, but fixing is hard in old frame so I went from an assortment of 5 colour old frame cards I like to Grixis dragon reanimator with OG Bolas at the helm. Deck is a lot more focused and consistent as a result (don't get me wrong though, it's still shit), but still uses only old frame cards.
Sultai graveyard. Everyone has had a Sultai graveyard deck at some point, right? So far I've done Sidisi, Mimeoplasm and Tasigur, and now I'm back on Sidisi with a dredge sub-theme.
The best example is my Aristocrats deck. I FUCKING LOVE Aristocrats. I used to run mono black with Yahenni at the helm. My god was that deck hateful. It was so mean. It was just edict effects and hand attack and soft locks stopping people from getting any sort of presence in the game. I loved it. My friends and I play casual jank though, and it was just too much. I pulled a
Queen Marchesa from a Mystery Booster (remember when paper drafting was a thing? Those were good days), so I took the plunge and built Mardu Aristocrats instead. Felt bad to say goodbye to my favourite deck, but it was for the benefit of the playgroup so it was worth it. Mardu is my favourite 3 colour combo, it lets me play all my old favourite cards like
Falkenrath Aristocrat and
Butcher of the Horde and the Monarch mechanic is just fun for the table. The deck is still strong in my meta and it still has a decent win rate, but my playgroup have a lot more fun playing against it so it was definitely a worthwhile change.