I think it's more about making sure, as narrator, that it feels like each challenge truly matters and impacts the story. If you find that players are dropping their "less favored" cards on particular challenge types, that suggests to me that there's something about the construction of the challenge that makes players believe it will have less impact on the story. Look at how the outcomes are written, and see if you can figure out how they seem to mean less than the outcomes that are physical.

One big thing: make some plots in the game resolved with a non-physical challenge. If players understand that plots won't always come down to a big fight or something like that, they'll be more likely to play all challenges in a similar way.

Additionally...it sounds like this is describing a setup where players want to ensure they're getting a Strong result all the time on challenges that "matter." That may be something to look into as well. Storium games go better when players aren't afraid of getting Weak results - when they're able to look at those as just another part of the story, not a punishment or penalty for some kind of failure. Take a look at how the outcomes are written, again, and make sure that both Outcomes for a challenge feel interesting. If the Weak outcomes for a challenge commonly feel punitive, you'll get players pushing for Strong results more commonly.

I think overall I've found that if you have challenges that always seem like they'll impact the story, and for those challenges, Weak outcomes feel interesting and move the story forward, you'll find less trouble with players "holding back" or "burning cards" on challenges to save them for "more important" ones.

On the actual suggestion...I'd rather not have the split, myself, as that split would basically require characters to have abilities in both categories. If I'm playing a scientific genius with a stick-thin body, for instance, I may not feel it's ever appropriate to really give my character a physical strength. Instead, he should have to figure out how to use his mental strengths to help out in unusual situations. Similarly, if I'm playing a diplomat, I might not be good at anything related to physical scenes. Or, if I'm playing a big brute of a warrior, maybe my only social cards are weaknesses. It's certainly possible that any of these character types could have Strengths/Weaknesses in different "categories," as well, but players shouldn't be forced into it--they should be playing the character they want to play.

Well, this sounds more like a human issue than a mechanics one to me. If you have concerns within your games about how challenges are structured or how strengths and weaknesses are played, then maybe just a conversation with your narrator/fellow players would help?

here is a link: https://storium.uservoice.com/forums/211322-general/suggestions/5763688-customise-game-parameters

not sure if its the answer but wanted to let you know.

arrgh, cant edit, I agree that a system that would allow players to forgo creativity for convenience really takes away from the experience, but I don't know if this is how to go about fixing it.

The perfect game would have no defining rules causing each player to eternally one-upp one another(to whose character is the most bad-ass etc..) since theirs no limiting factor to bind them or more properly define them.