What are the pros and cons of practising figure-eight landings on perpendicular runways? This is just a gee-whiz question, I have no intention of doing this nor am I trying to get anyone's blessing on this.

Part of remaining current to legally take passengers up in a plane is having 3 takeoffs and landings within the prior 90 days. There are also night requirements requiring 3 full-stop landings within the prior 90 days.

Some folks who don't fly often but want to take passengers up will hop in the plane and do 2 touch-and-goes and a full-stop before picking up their passengers. Those same folks might like to be thrifty and do those laps of the pattern as quickly and tightly as possible to minimize tach/hobbs time.

Here's what I'm getting at. If you were based out of an airport with 2 near-perpendicular runways, the winds were calm, and the traffic was nearly if not completely dead, could a pilot do figure-8 shaped landings so that the traffic patterns were halved? This would obviously involve alternating between left- and right-traffic, so those considerations would have to be made as well.

CONS/RISKS:

At an uncontrolled airport, there is some risk of surprising a plane that's not communicating. However, that risk is really not all that different than normal uncontrolled operations.

At a controlled airport, you'd have to get the controller's permission. Unless there's a specific regulation, though, I don't see why they couldn't clear you to land on 09 after taking off from 36.

PROS:

The whole point of these takeoffs and landings is to ensure that you as a pilot are safe to land on runways in general. Taking off and landing 3 times on the same runway does accomplish this, but adding another runway in there makes the currency more "general", especially if there are differing runway surface materials, lengths, widths, etc...

I did assume the winds were calm, but if the winds were something like 5kts, you would also get the experience of having a crosswind. This is great because you might be taking your friends to an airport with one runway, which could mean you have no choice but to deal with a crosswind component. You don't want your first shot at this in 90 days to be with friends in the back!
There's nothing stopping you from doing this at an untowered airfield, at least in the US, UK and most of the places I've flown to. There just isn't any benefit. What you should be looking to do is keep up the practice you need to fly safely, which is the spirit of the law rather than the letter of the law which is to maintain currency within regulation. 

Could you fly some weird-ass pattern and save about 5 bucks? Sure! Does cutting corners make you a pilot I'd fly with? Absolutely not, because you are looking for ways to economize rather than fly diligently. Flying the pattern is good because it puts you where other pilots expect you and keeps you out of conflict, it also means you know what to do when you arrive at an airfield for an approach. If you're constantly flying some strange bent figure-eight you're bound to mess it up and that could get you into trouble. Take-offs and landings are the busiest and most dangerous times when flying, the whole point is to standardize and reduce risk, if you are flying to a different runway every time the approach constantly changes which isn't good. A good landing comes from a good approach, which starts from a consistent circuit. 

Flying the same pattern is also good for your practice and improving your technique. Flying repeated patterns with the same wind conditions means you practice in those conditions until you nail them. It allows you to hone your technique. If you have a different wind, runway and visual cues every few minutes you don't get the consistency to learn what you're doing wrong and improve it.