I'm not an expert in this area, but this general idea that anything in math can be described as "intuitively true" is problematic IMO. It's not well defined, it's insanely subjective, and every math expert and enthusiast can come up with a ton of examples of things that seem intuitively true but reality is the opposite.

But if you just want *any* axiom that can prove CH, axiom of determinacy (which is incompatible with axiom of choice) can prove CH (but not GCH).