First of all, if you have a new house, don't you have a 5 year labor and 10 year parts warranty? I would never pay for an extended warranty on anything, but especially while the system is still under warranty.

Also, when a new refrigerant is required, you can still get the old refrigerant because it is recycled whenever a system is replaced. In fact, HVAC companies are required by Federal law to recycle any refrigerant that they remove from an existing system. They are not allowed to dispose of it. So, there will be plenty of the old refrigerant available for many years.

By the way, I have never known someone who replaced their HVAC system prematurely because of the cost of refrigerant.

I had AHS in Ohio as did my son on his home. Over a 7 year period I had multiple furnace repairs, a built in microwave replaced, fridge ice maker repaired, AC air compressor replaced, and probably a few other items that I can't remember, at that time we were paying between $400 and $500 per year and it was well worth it. My son had a upgrade policy because of the type of appliances he had and his fridge went out so he got the max allowable on that which was $1,500.00, he also had several repairs while he lived there. The difference down here is that most of us have only one AC unit whereas up north we had 2 of just about everything so if one broke down and we had to wait a couple days it was not a big deal. Our home was new here so at this point I haven't considered getting another policy. I would not get a car warranty, I like to get a new one as soon as the bumper to bumper is over and let someone else worry about getting things fixed.

I have always found that household appliances usually have a one-year manufacturer's warranty, if it gets through the first year without fault, usually things die of old age.
No to buying a warranty