In all the games I've kept a pick up Pokemon in my party, I always end up forgetting about it for long stretches of time and not getting much more out of it than a few ultra balls and maybe a nugget. :\
Pretty much this. I'll keep my pickup user over most other pokemon until I have 4 or 5 pokemon from my final anticipated party and really need the spot. It's always useful to have early Great/Ultra Balls, Rare Candies (even if I never use them?), and Nuggets or other high-selling items.