not all video games are first person shooters people....

In an ideal world that would be the case. Practically speaking though, there's a reason why we don't see this more often. It's no simple task.

They [i]are[/i] smarter on higher difficulties. Just like what senior said, they sidestep and take cover more on higher difficulties.

There is such a thing as too much enemy intelligence. A computer that has perfect aim and perfect knowledge of the map and perfect communication with all the other computers could easily be overwhelming. Thankfully Perfect AI are extremely difficult to create, it's much easier to simplify the various problems they face to make it easier for them to handle things and it introduces a certain amount of "stupidity" that makes things more realistic. How many settings should there be? The more you study Game Design, the more you'll find that there isn't a right answer, it is by no means a perfect science at this point.

I believe a smarter AI becomes a more challenging opponent, but I think they need some sort of flaw in order to a great AI in order to add a more 'alive' feel to the AI(not stupidity, rather something they can't do or the ability to miss, make a bad decision then try to recover from it or something of that sort). For your proposition they can make this flaw appear less(less bad moves, more precise movement, ect) In most games it would be more difficult to program an AI to be smarter to increase the difficulty without taking away from the easier difficulties(or so I think). If they could do it without losing anything, go right ahead, but I would imagine a difficult job is ahead of them.

All enemy characteristics should be improved if you ask me. Intelligence, abilities, damage, "rank", health and also numbers should be increased to make it challenging.