I'll answer this question in the context of a popular strength program (Starting Strength) that I happen to be doing.
Why only a few exercises?
Because as a novice, you don't need complicated training to make general strength gains. A well chosen, small set of full-body barbell movements trains you in almost every way you need to be strong as a human being. (For example: deadlifts, squats, bench press, overhead press, power clean, in my program.)
Many sets of each?
I think this is a false impression that you have. In my program, you only do 3 sets of 5 reps at the weight you're using for that day. There are possibly several warm-up sets that you do before your heavy weight, but those are just to prepare for the heavy weight.
Do the same program for a few months then change
Because if a strength program is effective, it will be useful for many months. I know people who have been on my program for up to a year before needing to change. I think you should use the simplest program that works for you. Eventually, when you get stronger, you may need more complicated scheduling to continue making strength gains, but the exercise selection shouldn't change much. I've been on my program for almost 3 months, and every workout, I'm lift more than last time. Why would I change programs?
For example, it should be better to do more exercises and fewer sets, or vary more often. (This was in the original question)
This is false. It isn't better to do more exercises, if you've chosen the set of exercises you do carefully. Varying the program more often than necessary is wasteful of your effort and time.
Quite fixed intervals between sessions, 2-3 times/week (If 1-split)
This is because a good program will plan rest-days to allow your body to adapt to the work it did in the previous workout, so that you'll be stronger in the next workout. For example, since novices can recover with a single day of rest, doing a full-body workout 3 times per week is pretty standard.
For example more variation in exercises could give a more "practical" fitness
This is incorrect. Variation for variation's sake is not more "practical". If somebody is only doing overhead press, then yes, more variation is needed in that person's program. However, if you've chosen an appropriate, small set of exercises and you are alternating between them during your weekly training cycle, you don't need more variation.
one set of each exercise could be more optimal for a beginner when time matters and the goal is fitness, not to prepare for more training.
One set of each exercise is not optimal, because it would be very hard to progressively stimulate adaptation with a single set per workout. If your goal is fitness, but don't do enough work to stimulate an adaptation, that is not optimal.
i want short-term results, not to build towards being able to train like a bodybuilder
Strength training is about making long term structural changes to your body. In my case I'm motivated to become better at my sport, but it's not just for athletes, and it's not just for bodybuilders. It's part of being a healthy human being.