Rig rentals only make sense if you rent at the right price and then mine the right coin on the right pool or mine a specific coin like @jacobw said.
For example. Let’s assume you want to mine Peercoin. The coin has a net hashrate of approx 270 TH and is usually the 2nd or 3rd most profitable to mine after BTC. However, since the net hasrate is “only” ~270 TH you can (if you want) rent up 20-30 TH and mine the coin and you will find blocks since you’re taking over 10-15% of the coins net hashrate.
Coinwarez has a great calculator to calculate profitability and help you in deciding which coins you want to mine. Personally I also prefer to rent power from NiceHash rather than BetaRigs.
If you compare both sites you’ll find that the avg price per TH is usually approximately 0.0130 BTC / TH per day on BetaRigs and anything from 0.0120-0.0125 BTC / TH on NiceHash. If you rent a few TH that’s quiet a difference.