Whilst I agree in principle, and yes, the "tab" button is often useful, not all programs work like that. Sometimes, pressing tab after your email/user name doesn't take you to the password box. Obviously, it's always worth trying to see if it does, though!
It's a great shame that there's no real standardisation in the writing of programs and apps. For those of us who use lots of different programs on a daily basis, it's quite annoying to see that very simple but effective shortcuts are not universal across different programs.
One of the most commonly used programs in our firm is actually a very old dos based program (now adapted and re-written to work under Windows, but it's still written as if it were dos with the same functionality it had as a dos program), where there are lots of "key-stroke" shortcuts that don't need a mouse (though you can use the mouse for all of them as well). We use it because it's exceptionally quick for data entry as you can keep your fingers on the keyboard rather than constantly moving your hand to the mouse! When I say quick, I'm talking about 5,10,15 times faster for data entry than using a mouse or touchscreen! When we have to use modern programs that do the same (i.e. where the client has chosen their own modern software which we have to work with), it's painfully slow to have to use the mouse or touchscreen and we really miss all the keystroke shortcuts.
Not talking about specific keystrokes for the particular program. I'm taking very generic stuff, like using the + or - key to move a date forward or back by a day, or entering a date from the keypad as 161023 whereas the modern program requires you to select the date from a calendar (or those awful scrolling lists on apps).
I do wonder if shortcuts were more universal and common, whether they'd be more likely to be taught in schools. As usual, though, schools aren't consistent in how they teach, so won't all be using the same software. They should, but they're not!