I know I can ctrl-pgup/down in Firefox (it's the best alternative to alt-tab afaict) but on one of my laptops it's incredibly impractical (pgup/down is way up the top right), and on the other pgup/down is in a practical, but very different, location to tab so it's "disjointed" in my mind (ie "do I want to go mru? ctrl-tab; do I want to go ltr/rtl? alt-tab" they're still in the same area, and hence it seem logical/simple to switch between those options often, whilst pgup/down seems very different?)
(And then meta-tab is also hanging out there, being simple and ready for an alternative context switch (mostly browser <-> terminal).)
Sure, but there's way more distance between Ctrl and PgUp then Ctrl+Tab (I'm taking a classic desktop keyboard in the account now). There are quite some more compact models where PgUp/Down are between the NumLock and - on the right side with the Numpad.
Not to mention you'd need to set the hand from one end of the keyboard to the middle, just to press something you'd otherwise move 1 key.
It exists for ages already, though. You use the same shortcuts to cycle tabs in dialog boxes. And that goes back to at least Windows 95, if not further.