Well, for starters, I'm no Doctor BUT I know that it's possible to develop leg, back, neck, nerve, and whatever-else problems if you do a lot of standing on a slab. My Father is a perfect example. He use to be a Type Setter which required 8+ hours a day of standing. BUT, let's see if I can somewhat 'enlighten' you on your options.
I'm sure that a slab is best for what you want to to so you have to ask yourself: Are you going to be doing a lot of STANDING in your house? If so, is the use of 'mats' or runners where you do the standing of any 'benefit' as far as minimizing the aforementioned problems? Depending on how you answer, you might have already answered your own question(s). BUT, if not, read on.
Radiant Floor Systems aren't limited to being installed in slabs. In fact, they are installed ON TOP of wooden subfloors as well as beneath them. This would imply 1) you don't necessarily have to have a slab to do what you want, and 2) that you can install carpeting as your finished floor. What you might want to do is talk to a few sources to gather some information. Talk to your Contractor/Builder about slab vs. wood subfloor (+ carpeting / hardwood finished floor.) And also talk to a Radiant Installer about the same. And a Carpet Installer and a Hardwood installer. I'm sure you'll get the thumbs-up from ALL of these sources but be sure to talk mostly with the Radiant Installer about 'his system' being installed 'under' YOUR finished-floor-of-choice.
Here are some links that may be of use to read:
Radiant System Under Hardwood Flooring NOTE: Your choice of wood is important. Maple is 'unstable'. Engineered flooring may be better. Ask about stability w/your contractor ... Rapid Radiant NOTE: This system is being installed over a wood subfloor. (Look at the picture.) Sooo, you don't necessarily have to have a slab to get what you want. AND, notice how far from the wall the tubing is. Hence, carpeting can be installed ... RadianTec NOTE: Here's an Under Subfloor System w/a comment about it. (It's to show you it can be done.) I know that the tubing today is 'designed' to bend easily between 16" joists OC ...) Radiant System Comments NOTE: Self-describing ... Radiant FAQ NOTE: 'Know' the source of who's presenting this information. (It's NOT the Gas Company ...) More FAQs NOTE: Again, know the source ... Radiant Heat and Hardwood/Wood Flooring NOTE: Understand the 'limitations'. (Ask questions ...) Radiant Article NOTE: Good article! The caption next to the picture states that this 'system' is 'ok' for wood or carpet finishes ... The Jen-Weld Family of Products NOTE: This is a vendor ...
There is TONS of info on the WEB about Radiant Floor Systems. As you can see, you have options. Learn as much as you can from different sources. Trust no one source (for information), and play one against the other to get the 'ins and outs' of what's best for you! Of course, trust yourself when you decide.