I don't cross train, but I go to the gym at times (been lazy lately).
The only reason I exercise at the gym is that practicing Aikido in the dojo does not help me lose weight. Got a spare tire around the waistline. I know... I know... Budo advises us not to over-eat and not to consume things that harm us. Guess that's why I need to practice outside the dojo.
The more I practice Aikido, the more relaxed I feel. So Aikido is becoming less and less of a cardiovascular activity for me (actually it never was). So I go to the gym to get my workout.