Why is a proper road bike pedal preferred for road bikes?
Hmm, we're kind of hitting most of the answer but not all of it (in my opinion that is!).

Its probably better to ask this the other way round - why not use a road pedal on a mountain bike...

On a road bike you're generally going to keep your foot in the pedal, you're only going to take it out to stop so therefore you want it to be as simple and as light as possible.

On a MTB you're liable to have your foot on and off more often, you're also likely to want to be able to stomp your foot onto a MTB pedal and have it stay there so it needs to have a larger platform area. You could also make an argument about MTB shoes being softer but the designs tend to be driven by competition and so that's probably more coincidence than anything else. If we're talking about using toeclips then clearly you'll need bigger pedals and clips for MTB boots than road shoes.

And weight does matter - it may only be a few 10s of grams but a few here and a few there will add up and all other things being equal less weight will make a difference.

I use clipless pedals - which I recommend - and I have one pair of shoes that I use on all my bikes, some of the pedals are fairly minimal for road, some clearly MTB, some hybrid but more MTB than not and all work with the same SPD cleat. Paradoxically my current setup has double sided pedals on the "road" bike and single sided on the MTB type pedals on my shopping bike...

So why road pedals? Assuming clipless and further assuming that you will only wear cycling shoes then you don't need the "complexity" (no difference in my pedals) or the weight of a full platform - so why have it? But the real difference will be in the shoes you chose to use.

(As I final thought I actually have two pairs of shoes - one waterproof - and a pair of sandals and they all have the same cleat so that I can use whichever is appropriate to the weather on whichever bike I happen to be out on.)