Did the importance of taking heads in combat contribute to the Japanese preference for cutting swords?

I'm not saying this definitively, but I am going to guess the answer is "no" because, as I understand it, they generally decapitated people after battle (for presentation ceremonies) and used a shorter tanto or wakizashi for doing that and the tachi and uchigatana still were curved.

I think the curve is at least a couple of factors: One is that the differential hardening process causes straight swords to curve (and curved swords to curve even more). Another is that the uchigatana comes from the tachi and the tachi was a cavalry sword and they liked a long curved blade for that purpose. When they moved to more massed infantry as the sengoku period dragged on the uchigatana appears and becomes straighter (generally) and shorter but the curve stayed. Indeed, many tachi were shortened to be uchigatana. So it might just tradition - their martial tradition was already entrenched to use curved blades.

Completely speculative on my part - I am no expert.