Westcott and Hort's work did not appear out of the blue. There were numerous attempts to revise the printed Greek texts prior to it: polyglotts (like Walton's), Griesbach's work and Tischendorf's, to name a few. In addition, many, many commentators and scholars had made notes on where they thought the best manuscripts differed with the then commonly printed Greek text.
I would say the vast majority of Christian textual scholars and Reformed commentators of the day and prior centuries recognized that there were problems with the Received Text, although there was not an agreed solution. Certainly the Princetonians (Hodge and Alexander even before Warfield) recognized issues. Westcott and Hort was just the first revised text to find some kind of general acceptance during that period.
Their work was produced and accepted because there was a growing consensus that it was needed.
Thanks. I would love to hear more about this. Can you write more or direct me to books or links?