There's nothing wrong with downloading mods from Steam, this insistence otherwise strikes me as a bit of an elitist attitude. Yes, their system could still use improvement, but it *IS* a proper tool for installing mods, and the official launcher, crude as it is, is a proper tool for managing mods. Yes, it too could use improvement, but it DOES work.
The SKSE website does not specifically say to use the version from the Steam store. It's just a recommended option should other methods not work properly. IMO, the best option would be to use their exe installer from the site. The Steam Store version hasn't been as thoroughly tested, and the manual install archive is probably best left to more advanced users.
Of course, this kind of thing depends on where you put your Steam folder too. If it's in the Program Files folders, you probably should move it because that's known to disrupt the ability to mod the game because of UAC.