Why can’t the CF34 use wide-cut fuels?
Actually, the CF34-3B1 engines are certified to use wide-cut fuels, JetB/JP4. This comes straight out of the AOM for the CRJ200. I would venture to guess that all variants from CF34-1A to 3B would have the same certifications.

The CF34-8C5 engines on the other hand are not, again straight from the AOM for the CRJ 705/900. CF34-8C1 to 10E also likely have similar certifications for fuel certifications.

The difference is likely more to do with cost to certification. Seeing as wide-cut fuels aren’t overly common, except in the most remote locations north of 60 degrees of latitude, GE probably said why bother spending the extra money. JetA1 is good to -47*C/-53*F so for most commercial aviation, it’s more than sufficient. Every aircraft I’ve flown to date had an on-ground operating limitation of -40*C anyway.