Math is full of specialized problem-solving skills. Like, "oh, this seems to fit the pattern where we can integrate by parts". If you don't know that, you don't even know that you don't know that; it's an unknown unknown.
General problem-solving skills aren't a substitute for special skills.
General problem-solving skills have limits; one of the outcomes of general problem solving is the conclusion "I don't know how to solve this; it may require someone with special skills".
Without properly honed general skills, you may waste time avoiding this correct conclusion (among other mistakes). General skills let you undestand what the problem actually is, what a solution looks like, and whether you are getting closer.
General problem-solving skills aren't a substitute for special skills.
General problem-solving skills have limits; one of the outcomes of general problem solving is the conclusion "I don't know how to solve this; it may require someone with special skills".
Without properly honed general skills, you may waste time avoiding this correct conclusion (among other mistakes). General skills let you undestand what the problem actually is, what a solution looks like, and whether you are getting closer.