Why use a sandwich press instead of an oven or pan? I often make hot sandwiches. Usually I just put butter on the outsides of the bread, then put them in the oven just until the cheese melts. I see other people just put the sandwiches in a pan with butter, and flip it a few times.

I notice the store selling sandwich presses, but am confused by the purpose. They do not seem more convenient than an oven, because that just adds another item to wash, and they seem to smash the sandwich.

Is there some advantage to using a sandwich press in terms of convenience or of taste?
There is really no advantage or disadvantage to using a sandwich press. This is more a choice of preference from person to person.

For me, a sandwich press is preferable as it toast the bread on both sides simultaneously, so you get an even toast on both sides, and it also presses the sandwich together so that it does not fall apart. A sandwich press also heats up faster than an oven (note, I'm talking about electrical ovens that is commenly used in RSA) and consumes much less electricity to do the same job.

So yes, this is all about what you prefer and what works best for you