Berkeley wasn’t the only one to criticize the foundations calculus. And insofar as his criticism of calculus goes, it is IMO hardly more philosophical rather than mathematical compared to criticism from mathematicians like Rolle. Insofar as the “philosophical” side of his argument goes, the general shtick behind Berkeley’s criticism seems to be the desire to show that the foundations of religion were no worse than those of math (he was a bishop after all). So I don’t see how his philosophical insights could help math to develop.
First, you're right about Berkeley's motivation. Specifically he was rebutting Edmund Halley. But his criticism was correct. And he was also correct that through compounding errors mathematicians arrived at truth, if not science. Furthermore he demonstrated that he had a better grasp of calculus than most who criticized him at the time.
You're also right that what he said could not help math to develop. But that is not due to any shortcoming on his part. Until mathematicians realized that there was a crisis, nothing could have made them pay attention. And once a crisis was realized, what would help them find a path forward depended on the details of said crisis.
Now you pointed to Rolle. Yes, Rolle criticized infinitesmal calculus. But he did so before it was well understood, and all of his criticisms were rebutted. In fact Rolle wound up convinced about calculus, and is known for an important theorem. (That said, his original version was considerably less general than the current one is.)
He was not alone. Lagrange also criticized calculus. His alternative was to found everything on formal power series. But his replacement didn't hold up. In fact Fourier's examples were more of a problem for Lagrange's approach than infinitesmals! So from Lagrange's criticism we got the f'(x) notation, but nothing that could help later.
Lagrange's failure to be able to address the future crisis, even though he recognized the problems that lead to it, demonstrates that Bishop Berkeley never had a hope. Lagrange was one of the top mathematicians of the 1700s. If he could not anticipate what would be needed, how could a bishop be expected to do better?
