Actually, those MKS cleats have a prong on the front that inserts into a slot in the front plate of the pedals, while the main rear slot on the cleat drops onto the back plate of the pedal. This means you are pretty well locked in place once your toe strap is tightened -- no sideways slipping, no tapping of the front part of the cleat on the pedal. It feels essentially as solid as a Dura Ace 7400 does but without the problems of the 7400 cleat. MKS is changing their other pedals (slowly, because this is NJS country) to use the cleat as well, but the RX-1's are fine for almost any purpose.
Riders for many years rode stage races and everything else in toe clips and straps. I grew up that way. When you're used to it, you just reach down and flip the strap loose -- it's automatic and while not quite as fast as clipless pedals, it's pretty close and pretty easy. I wouldn't necessarily encourage reactionary thinking just to ride old-style clips and straps instead of clipless, but it does work fine. Bear in mind that you have to keep the slots on the cleats free of dirt or they won't seat properly and will also grind up your pedals quickly.
Many match sprinters and other power riders still like to use clips and straps like that. When you strap in really tight, your foot is clamped down to the sole of the shoe, which is clamped down to the pedal. Nothing is going to move. The tension over the top of the foot isn't comfortable for some people and they have gone to pedals like the Dura Ace 7701 SPD-R, which has an extremely strong and reliable clamping system with an all-metal pedal that will never break or give problems. For most riders, including those riding longer events or massed start programs, these are probably just overkill -- you can use standard road clipless pedals and not have any adaptation from road to track bike.
If you are considering these on a road fixie, perhaps the biggest (albeit petty) issue about clips and straps is that on the road, you chew up cleats, straps, and clips fairly quickly (compared to the track), so you just have to replace parts more frequently. It's not worth buying cheap straps -- I'd encourage at least MKS Fit-alpha's and ideally Toshi's if you want long and reliable life from them. But on a road fixie you don't need the gripping power and freedom from stretch that you want on the track. In contrast to a couple other comments above, I wouldn't say "no" to clips and straps, only "why?"