In Europe there was deep opposition to secular instruction.
For most of those hundreds of years, the deep opposition to secular instruction came from the non-Jews who opposed admission of Jews to their institutions. Is this the tradition they're keeping alive?
Um... Volozhin 1792?
The Volozhin Yeshiva had what? 50?...100?...400? students a year, at a time when the Jewish population of Russia was 5,000,000.
You might argue for reforming American yeshivas so that they resemble that format, but it wouldn't be accurate to say that that was ever the traditional educational experience for East European Jews.