Without exterior vent, your pulling warm moist air and dumping it into unconditioned space. 

Basements are often moist. 

Its hard to explain, but I looked at a place which had a leaking roof and when you walked in it felt like walking into a greenhouse, moist.

What makes mold is not heat,, it is dark / moist un - circulated air that has the most issues for mold or mildew

So if keeping the soil moist is the solution to not having foundation issues, is xeriscape or that grass like stuff you have the better ground cover solution?

I had my place occupied 2 weeks after I finished it last December...and i got a tenant that pays his rent on the 1st (removes glasses to wipe moist eyes)

A/C units (3) are 17 years old, roof is 17 years old with skylights currently leaking, there is staining in some of the bedrooms that are near the bathroom showers, and the utility closets are moist and rusting.

The crawl also appears to be quite moist, since there weren't any vapor barriers set up to prevent moisture from building up.I am worried that over time the soil could shift, causing the supports to give way.

There is no comparison between the moist heat of gas and electric heat.

Roaches and other insects also like moist areas so maker sure your basements and crawl spaces are dry and well vented.