It's bizarre to me that rent-a-miner is a viable business at all. Why don't the owners just set the miners to mine whatever the most profitable coin is at the moment?
The "owners" of the hardware are private miners. The rent-a-miner business (NiceHash) just connects sellers of hashrate (miners) with buyers of hashrate. The miners don't care what they are mining, and they get paid in BTC regardless of what their hardware actually mines. NiceHash is just a marketplace that automatically mines the most profitable coin by what people are willing to pay for hashrate. None of the hardware belongs to NiceHash.
Your question is still valid and good, but not in the way you have phrased it. The real answer is: laziness. NiceHash is easy and steady. If you have a nice gaming rig, you can make a few extra bucks a day by selling your hashing power while it's idle. If you are a serious miner, you probably don't use NiceHash.
Aren't the owners doing exactly that? Whatever is the most profitable coin is determined by the buyers of the rent-a-miner market and the sellers get paid that, less the cost to the market-maker for that discovery. How else could it be?