Another reason to use veneer has to do with structure. When you make something like a serpentine dresser, how do you make that curve and make it look right? The answer is to use veneer. You could use solid wood, but it wouldn't look right. Why not? You would see the end grain, not the long grain that is pleasing to the eye. That method also will waste a lot of really expensive wood, since you would have to buy a big board and then cut most of it off. You could bend the wood. That wouldn't show the end grain. But (and you knew there was going to be a but) bending wood has it's own issues. One of those issues is that the coolest looking figured pieces all have one thing in common. They don't bend well. So in the end, what you end up doing is coming up with your curved panel and then veneering over it. Now making that bent surface is a subject for a whole other post, so we will leave that for another time. We will leave it at you could use a wood that is cheaper and bends well and make a bent panel that way. Or use a cheaper wood and simply cut a large board to the right shape. Or you could use a bendable plywood made just for such an application. Any way you make it, you want the part you see to look good. So that becomes the part you veneer. And this way you can use what ever veneer material you wish. This becomes particularly important if you happen to be partial to burled wood. Burl is pretty, but that's really about all it is good for. It can't be bent. It isn't very strong. And it doesn't work particularly well. So to use it, you need to make a stable base under it and then veneer the burled wood on top.
Basically, what this comes down to is using the right material in the right situation. And this is something that you will hear me come back to often. With the use of veneer, you can use one material that will take advantage of that material's strong points and then give it what ever decorative covering you wish.