I always find it odd when artists apologize for drawing the same characters a lot.
Yes, this was prompted by a mutual's journal entry, but this phenomenon is far bigger than any single person and I've wanted to talk about this for a while.

Having lived through the past couple of years of adoptable apocalypse on deviantart, I can wholeheartedly say it doesn't matter how cool or interesting your character designs are, if I see a brand new face every week I will never get to familiarize myself with any of them. A good character design or ref can really make you interested in a character, but what matters more is that you see them doing other things too. You WANT to see characters in multiple drawings.
If you draw the same 1-3 characters all the time, your audience really, REALLY gets to know who they are as people and they start to care and get invested in those characters' lives. Isn't that what you'd want as a creator? For people to see the same cool things that you see in your characters?

I'm a creator with a relatively slow output and I unfortunately don't have an obsession character. My OCs are split into two sets of 30 or so guys and I have all kinds of things I'd like to say about all of them, art I'd like to draw for all of them. So I'm always fighting with the dilemma of "should I draw more art of this one that I like a lot so people get to know them and understand why I like them so much" versus "should I finish the designs and draw more art of these other characters cause they have even less work presenting them than these other guys, but that means taking my time away from those same guys who also could use more work presenting them".
I'm always fighting my focus. I WISH I had an obsession character cause then I would be drawing nothing but them and my audience would learn all of their quirks and things, and I would feel less like I'm sitting here alone looking at something I love so much yet other people can only see through little needle-sized holes.

If I had an obsession character I wouldn't be overwhelming myself wondering if I should finish character refs, finish the size chart, finish this outfit design, finish that redesign, finish this or that map project, expand on this lore or finish the illustration for that lore, start writing about this or finish writing on that, make this comic or plan that comic... Because as a result I do none of those things. I sit here rolling my thumbs because there is too much I could, should, do and motivation for all of them is relatively equal.

Enjoy your obsession characters. Never apologize for drawing the same guy every day. It's a blessing to both you and your audience.