If you're running one card per rig for multiple rigs, you're losing out.
As others have mentioned, more cards per rig is all about reducing overhead costs, that is, costs for obtaining and maintaining components that do not directly contribute to your hashrate (and thus revenue stream).
You purchase a CPU/motherboard/RAM/storage device/1 or more PSUs for each rig. At one card per rig, you're purchasing far more of those than is desirable.
Now consider what happens as you add more cards per rig. This usually requires additional or more expensive PSUs, and additional risers. However, the amount you put down for a CPU/motherboard/RAM/storage device remains constant. (Perhaps you might pay more for the motherboard, depending on which you select.)
Thus, in terms of performance vs. initial overall cost, you're doing better. (Think hashrate/[sum of all component costs])
Also consider performance vs. electricity costs. Each CPU/motherboard/RAM/storage device draws some amount of power at the wall. The fewer of these you have for some given number of cards, the better you're doing in terms of efficiency.
Of course, not everyone wants to put tons of cards in one rig. (For most of us, 6-12 seems to be the sweet spot.) This is because A) Setting up more cards in a rig tends to be a real pain, especially with troubleshooting, and B) Too many eggs in one basket is not a good thing. If a critical component, such as a motherboard, were to fail for any reason, then you would have more GPUs down until the component is replaced or the cards are relocated.
However, the vast majority of us would agree that more than 1 card per rig is ideal for a dedicated mining rig.
(There may be an argument to make if you happen to have several unused desktops, each with room for exactly one card, and you have free electricity. However, I would assume that this situation is rather uncommon.)
Agree with everything said here!
I like doing 8 cards per rig because I find that managing them is the sweet spot for Windows. If one fails, you're still at 7 while you get a replacement and troubleshooting is simple enough.