It's not at all universally true that business travel lowers your monthly household costs. If you're a very heavy traveler who is on the road 200+ business days/year (that is, pretty much all of them), then yes, you can have close to zero household costs because you can be effectively homeless. You can have a PO box or mail drop where you get mail and packages, and maybe a storage unit or two in strategic locations, but you have no household costs.

If you travel 50% time, get per diems, and are cheap, you can end up ahead, but not by much, and if you have much of a household some of your per diem goes into covering household expenses that might increase while you're gone (child care, pet sitter, house sitter, plant waterer). The GSA per diems for domestic travel are very reasonable, and even generous if you have a relatively inexpensive lifestyle to start, but if you have a home and family, you're probably spending some of the per diem on things at home you wouldn't have spent on, or you're buying things you need for travel (adapters, travel pillows, headphones) that end up amortized in that daily underspend. For some people, signing up for a 50% travel job is deliberate and they probably can minimize their costs at a home that they don't use much. For others (probably large fraction) it's a temporary situation inserted into an otherwise average lifestyle.

At 25% travel or less, it's very easy for the per diems to get eaten up on taking care of things at home that you'd otherwise do yourself because aren't designing your home lifestyle around a high travel job.

The gov't uses per diems to make auditing a whole lot easier-- they don't have to worry about tips (see the thread in omni), or whether someone bought some alcohol at dinner on gov't travel. The GSA rates are consistent with eating 3 sit down meals a day and not living on super cheap unhealthy food, and having a little left over to cover incidentals. This is a case where the gov't is doing something that on the whole is extremely reasonable and, while it's subject to minor exploitation, you're not going to get rich or live an extravagant lifestyle on what you save from eating on the cheap (which would eventually show up in the press and cause a fuss), so they don't worry about it.

See SuperAngryPenguin. He travels that much and still maintains a household at a home base with at least one other person living in it. How is the gov't to distinguish between him and the itinerant homeless business traveler?