I wasn’t around when the game was missing the Throw button, but I’m glad it’s gone. I saw the value of adding a separate Throw button when I moved from the 2D fighting game Bleach: The Blade of Fate to its sequel Bleach: Dark Souls.
The Blade of Fate let you throw with Forward+Medium or Forward+Heavy, which would throw if the opponent was close enough and attack otherwise. I used throws all the time against the CPU (the only opponent available), and fighting was often too easy because the opponent blocking had no effect on my attacks when I was close enough. To use terminology I have learned from Fantasy Strike’s documentation, my throw’s option select let me ignore the blocking mechanic too often.
Bleach: Dark Souls changed this to having to press Light+Medium to attempt a grab, with some recovery time if you missed. I didn’t have an opinion on grabs when I played the first game, but when I played Bleach: Dark Souls I soon noticed how it made the game more interesting by forcing me to pay attention to whether my opponent was blocking instead of blindly running into them and attacking.
However, that change to the Bleach games is not exactly comparable to Fantasy Strike, since blocking in the Bleach games is done with a dedicated button while standing still, not by walking away from the opponent. So your opponent is more likely to be in grab range in Bleach.