As a spinner fisherman, I fish upsteam exclusively and I stay in the water unless it is too deep to wade. I stay in the water and fish upstream because:
1) As you mentioned, trout typically face upstream, so by fishing upstream I am approaching them from behind where they are less likely to see me and spook.
2) It gives me the opportunity to present my spinner in a direction consistent with how trout are used to getting their food, that is, downstream with the current.
3) I want to fish a lot of the less productive-looking water between pools.
4) It decreases the odds of me encountering a rattlesnake.
5) I don't want to have to concern myself with muddy water that I've stirred up entering the pool I want to fish.
6) I want to maintain a low profile to minimize spooking trout.
7) I'm less likely to fall and hurt myself when not climbing up or descending streambanks.
8) I don't want to potentially spook trout every time I get back in the water.
9) I'm better able to minimize vertical line drag during the retrieve.
10) I like to retrieve my spinner with the current because it is easier to keep it down deep.
11) It is easier to set the hook than when fishing downstream and retrieving against the current. (Trout tend to just nip at a spinner when it is retrieved against the current.)
12) I avoid a lot of the deeper hooksets because my spinner is more often moving rapidly.
13) It makes it easier to read the water ahead so that I can decide whether I want to walk on the left, right or center of the stream to maximize my opportunity to minimize horizontal line drag.
14) It minimizes my exposure to ticks.
15) I'm less likely to puncture my hip boots on multiflora rose bushes, barbed wire, and other hazards.
16) So that I can cast constantly and stay in rhythm, similar to how a basketball player can get in rhythm and start dropping three-pointers one after the other. This improves casting accuracy and my hooksetting percentage.
17) So that I leave fewer footprints, which lessens the likely of someone realizing I'm ahead of them and having them loop around me.