Almost all road cyclists that I've seen use one or other variants of the clipless pedal system - special shoes with cleats mounted on them which engage bolts on the pedals so that the rider's feet are locked to the pedals. It's almost universal now, and many mountain bikers also use a mountain-specific version as well, which is basically the same idea except that the shoes are easier to walk in.
The idea is as follows.
If your feet are attached to the pedals, you can apply pressure all the way through the pedal stroke, by "pulling up" on the pedals as well as pushing down. This is said to be more efficient. Unfortunately, this is received wisdom - if anything, the reverse is true. If you're applying more pressure at different parts of the pedal stroke, you're using extra muscles for it. Those muscles need to be powered, so you're using additional energy to do that. You may be doing that to go faster - OK. You may be doing it to get up a hill - in which case a lower gear is the answer you're looking for. Those muscles you're using to pull up - the hip flexors, for example - are not designed to pull like that, they're designed to stabilise the foot, control placement on the ground and lift the foot over obstacles. You're just going to fatigue them pulling up on the pedals.
But then there's this. Cadence is one of the most important things to get right when cycling. That, together with the art of applying the minimum effort to go forward at the maximum speed. The absence of a low enough gear on many bikes, especially road bikes, is in my opinion the real reason clipless pedals are so popular. If you hit a tough climb, say above 8-9 percent, of any duration, your cadence can easily drop below the 80-90 rpm that most people seem to agree is the optimum for avoiding muscle fatigue (I've certainly found that's true) because you don't have any gears left. But if you pull up as well as pushing down, you can basically "find a new gear" and get up a hill that would be really awkward on flats. I do this all the time, because I have to. But people confuse this with efficiency; it's not, you're just using more power. That's the opposite of efficiency, which is about using less power. You do that with cadence, and an efficient pedal stroke, but not if you've already run out of gears. I live in a very hilly place, so I often run out of gears.
Then there's the incredible sensation of danger when you can't get out - who hasn't fallen over when training with clipless pedals, unable to disengage in time? Falling over at the lights is bad enough, but a real crash is truly scary. I still think people who use them for mountain biking are insane.
And what about foot position? Am I really the only rider who needs to vary his foot position if riding the bike for 6 hours? I understand some people have fitted extra mid-foot cleats to give them another option, but really...
And then - I discovered a use for them. I went to southern France, touring on my XC race hardtail. I got to the campsites, pitched the tent, dumped the bags and hit the trails in the Luberon mountains, the Nesque gorges, Mont Ventoux and the Vaucluse mountains. The MTB trails in this part of the world are mostly converted hiking trails and farm paths, they're very steep, and the entire area, including all the trails, is covered in fist-sized chunks of limestone. It's beautiful country but the climbs are brutal and the descents are terrifying - just because of the steepness and the fact that the whole trail is moving under your wheels in chunks 20cm across.
A constant problem with this type of riding is that your feet get knocked off the pedals - this is a problem I've never had before, but basically these trails were so rough I was really getting chucked about. They're not technical, just chunky and loose, and fiercely steep. Not my favourite type of riding I have to say, but the country just begs to be explored. Locking into the pedals really does help with this, although I do recommend disengaging on difficult descents - reversible pedals with cleats on just one side are a good compromise and will let you descend unclipped while having full control.
You probably don't need my advice, but here it is... learn to ride on flats. Take that pedal stroke to clipless. Don't push forward or back, just down. Don't pull up except when you have to, to make headway. Concentrate on pushing down in the stroke, and rest your trailing leg while it's coming round.
When you go out with packs, put your flats back on. Your tour bike will go over like a ton of bricks when loaded, as you know from all the dents on the side... and without the clipless pedals, you can do the whole trip with one pair of shoes and be comfortable walking around. Good flat pedals, like the ones for BMX or modern MTB pedals, have adjustable screws so you can dial the height for optimum grip. Lots of different types of shoes are available, I always wear trail running shoes which are about perfect, and they're great if you want to go for a hill walk too.
As you can see from the picture at the top of this page, on the adventure bike I do have XTR pedals most of the time, with MTB shoes. This is partly because of the gearing - you have to pull up to make decent headway on some climbs, even on sealed roads (Opau road, Horokiwi, Spicer Forest etc) and partly because it's a skill I did want to master, before rubbishing it completely. I'm just about there now; I hardly ever fall over.
OK; experiment over. I ran XTRs for a year on the gravel bike with a very nice pair of Giro shoes. They're for sale now. After trying both, I prefer platforms in every respect. On the flat and shallow gradients, I don't think it makes much difference one way or the other, but the flats are way better for steep climbs, and I've got much more control over the bike on descents. And overall, I'm sure I'm quicker.
And boy are these nice flats - I just put Specialized Boomslangs on the gravel bike, which have incredible grip, and Xpedo Sprys on the XC bike. These are incredibly light. And way cool...