When you said "defensive" I expected a lot of waiting around and reactionary play, but watching the Diddy vid I'd say if anything you're overaggressive. Pressing buttons even when there's no chance of hitting, landing on your opponent's shield with fair/dair even though that's incredibly unsafe, etc.
I'm unsure what about Pika doesn't feel like he's for you, but despite what you've apparently been told he looks like a good fit for how you play; you just need to refine your play. I'm no expert on Pika, but some stuff that stuck out to me: fade back with sh fair instead of falling on shields to make it safe, don't forget grabs/quick attack/pivot fsmash exist, maybe go deeper for bair/Thunder edgeguards (though for the most part the Diddy wasn't very far offstage and your patience on the ledge + punishing his decisions to recover onstage was the right choice), etc.
Essentially, I think you feel stuck because you have the character down at a surface level. Now for improvement you need to be analyzing what you're doing, ironing out the wrinkles, and asking yourself what things you're doing wrong and how you could do them better. Work on spacing, think about what each option beats and when it might be best to just not commit to anything, and so on.
Though I guess to answer the original question,
Can a character you like, simply not be for you?
Yeah, definitely. I like
, but I'm garbage at playing them. I was also that way with
initially though, and it wasn't until I started utilizing her toolkit better that she began to click for me.
