Yes, there are circumstances where a tripod isn't practical. But where it is, using one is better than not using one. I set up tripods on the streets of Toronto all the time. No problem.
You're misunderstanding the use of Exp Comp as I'm suggesting it. Using exp. comp. to adjust the metered exposure for the built in bias (with most matrix type meters now this isn't necessary in many circumstances; they're that good) is different from using it to create a wider bracket sequence. And no, I wouldn't suggest using exp. comp. to adjust meter bias when doing HDR. As noted, today's multi-segment meters are so good that it's generally not necessary and shooting in Manual you set the exposure where you want it anyway. What I'm getting at with using exp. comp. in bracketing is to use it to get a wider bracket. For example, you've got your camera set up to do a 2 stop bracket (-2, 0, +2). If you dial in -2 exp. comp. and take one sequence you're going to get -4, -2, 0. If you then dial in +2 exp. comp. and take a second set you're going to get 0, +2, +4. Toss out one of the 0 shots and you've got a nice 5 shot bracket with, in almost all cases, enough exposure to cover the entire scene. Same thing applies if you're doing a 1 stop bracket (-1, 0, +1). Dial in -2 and you get -3, -2, -1. Dial in +2 and you get +1, +2, +3. No zero shot? Not really a big problem but you can shoot the single 0 shot before you start the brackets or after you're done.
Sure, the align functions of most HDR software apps are quite good. But if the input shots are misaligned, you're going to have, at the very least, problems at the edges and there may be a need to crop. If you've got rotiation rather than just vertical/horizontal movement the problem is exacerbated. Shooting a bit looser composition will make up for that (horizontal/vertical movement) but you're throwing pixels away. The deghosting process of some HDR software doesn't make up for misalignment. It's intended to make up for things that may be moving during the shot in the scene, not for camera movement. Some are better than others but none are perfect. And no, you don't need to use TIFFs for the align functions of HDR software to work. The Align Layers function in PS is different. That's not what's used in aligning input shots in HDR Pro.