First, electric heat is the most inefficient heating source available - you are taking a KW of electricity and converting it into a KW of heat (unlike a heat pump, which takes a KW of electricity and uses to pump 2 KW of heat into your home).
So resistive radiant heat has its own set of issues. I am not sure that the combination of these two expensive systems would result in a cost-effective HVAC system. When you add up the cost of all those individual split systems, plus the cost of electric radiant heat, you end up with an installation bill that is 2x to 4x higher than a basic heat pump forced air system. In order to recover those costs, it would take years - if ever. The ultimate operating costs might be a wash or even higher when you have multiple expensive systems to repair.
We didn't have many problems with the split systems, of course. But since we had four systems, that was 4x the chance of failure. The Mitsubishi system that came with the house ("Mr. Slim") worked well even though it was about 10 years old. The cylindrical fan on the inside unit did shatter in places and I was lucky to be able to find the parts diagram online, google the part number, and find a replacement fan for fairly cheap and install it myself (once the blades broke, the fan would wobble at high speeds and make noise). So I can't say these are maintenance-free units. And since you didn't work as an A/C tech, maybe this level of maintenance is not your bailiwick.
One argument made in favor of split systems is zoning. You can shut off the units to rooms not in use and thus save energy and money. That sort of works, of course, but it is the same argument made about electric fireplaces - you only heat part of the house. This does not mean the underlying method of heating is more efficient, of course. And in fact, with electric fireplaces, just the opposite (resistive heat, again, literally burning electricity to make heat).
You can just close ducts (registers) in your home to achieve the same effect with a central HVAC system. So I am not sure the zoning thing is really a selling point - or one to justify a 2x-4x price delta.
So why do people use them? Well, if you have an historic house that you cannot cut up to put in ductwork, they make sense. If you have a house with no central air (as I had) they might make sense (particularly if you get them grey-market for 1/4 retail and install them yourself, again not recommended for the unhandy). If you have an addition or converted garage (as my neighbor has) with no ductwork installed, a split system can be an easy way to add A/C.
But absent these compelling reasons, the split-system makes less and less sense. Today, many contractors are pushing these as a high-end HVAC system, much like the built-in refrigerators and restaurant-grade stoves (or their lookalikes). The idea is selling status and luxury. And many people are buying them, convinced that "more expensive is better" or at least is more impressive to show off to friends and neighbors.
It is like the folks who ride a bicycle once or twice a year and go down to the boutique bike shop and buy an expensive racing bike costing thousands of dollars. It is a "better bike"? Yes, for certain applications. When Mom puts her flowered basket on the front of the handlebars, however, and uses it to ride to the corner store, it is kind of ridiculous. Like delivering pizzas in a Ferrari.
There is such a thing as appropriate technology.
Would such a convoluted HVAC system "add value" to the house? Maybe, maybe not. Generally, the value of homes is determined by the location and number of bedrooms, period. You can fancy up your house all you want to, but if it is in a bad neighborhood it will not be worth much. Similarly, a basic house in a good neighborhood is going to be worth about what the fancy houses are, particularly if it has more bedrooms. You can always add fancy. But for every dollar you spend on fancy, you would be lucky to get back 50 cents in added retail value.
Expensive HVAC systems are like any other expensive home appliance - you don't necessarily get more for your money, other than bragging rights. And it is kind of hard to brag about an HVAC system, unlike say, a fancy stove or whatever.
And quite frankly, having a big box hanging off the wall in every bedroom of the house is kind of ugly. Oh, and be sure to change the air filters on all of those units on a monthly basis, right?
Sometimes less is more!
EDIT: Prices for split systems have gone way up since I installed mine. A basic unit these days is $1000 online, and that does not include installation. This is a cooling only unit:
Larger units are $2000 and up:
Again, not including installation. So to cool your basic house, with a unit in each room (some units have more than one "head" of course) is going to run at least $10,000 or more, particularly if you have a multi-story house with long refrigerant runs.
They are lovely HVAC units. The Lexus of air conditioning. I drive a KIA and it works just as well.