Well, if we do go with Kaoruko defeating and banishing him years before Ulquiorra will almost certainly have some interest in her granddaghter, though after seeing her in action he'll likely be pretty dismissive toward her low level of skill. So, if you want somebody around to hurl barbs at her about her weakness and how she can't possibly overcome them, he's your guy.

Plus if Tsubomi does hold onto that idealistic optimism of hers he might take interest in that, if only to attempt to extinguish it because what she's saying can't possibly be the truth. I'm open to Tsubomi playing a part in ultimately defeating him and maaaybe getting him to rethink his outlook... right before his total death, naturally.