Seeing as you left it so long before completing it (and could have beaten the game without doing so), it obviously isn't mandatory.
The only mandatory shrines in the game are the four on the Great Plateau, with the entire area essentially acting as one giant tutorial... if you want to complain...
If they'd just set up the tutorial to run during your first trial of strength, that would probably have been the best way to do it.
Putting it on the Great Plateau would take away the chance for people to discover those mechanics for themselves.
But I don't think putting it in the Kakariko...