Personally I don't care for a conditioned crawlspace. I do not like the idea of mixing crawlspace air and house air. I'm curious as to what they are doing for make up air for the loss into the crawlspace.
My .02, I prefer to have the crawlspace in a negative pressure so that any sewer gas from a leak, radon/methane from the ground, as well as the odors from dying/dormant mold that hasn't been physically removed is going to produce and then be mixed with house air.
I would rather have a dehu dedicated for the crawlspace which costs much less to run than the Hvac unit to remove and maintain that moisture.
As well per the code, on larger crawlspaces, ie cubic feet of contained air, if you condition the space, the Hvac unit has to be sized larger. Not only does this cost more upfront, but then the units typically short cycle and do a terrible job of removing any moisture from the air.
They run, change the temperature of the air to meet desired level, and shut off.
The main problem I have with that scenario is the major amp draw of the start up of the compressor when the unit is short cycling. This usually is much less efficient than a smaller sized unit running long enough to change the air temp and remove the moisture.
The code addresses the three types of crawlspace currently allowed.
Again just my .02, a lot more factors need to be accounted for than just allow a 4" supply to the crawlspace with a damper and call it good.
Typically the energy savings of having the space air sealed make up for the energy cost of running the dehumidifier, if it is sized properly.
My last consideration: why would I pay to condition a space that is not lived in? The loss through the duct system insulation once the space is closed is enough to keep the crawl space temp 65-75 degrees year round.
Even on houses without insulating the foundation walls, only air sealing the walls, and it is a closed crawlspace not conditioned, with an outside temp of 28 degrees and snow covered ground, the crawl space temperature remained at 67 degrees.
This house met the new code requirements for air leaks and insulation.