Batman wrote:The enemy being able to ignore your shields is exactly the situation where you want to pour it on as much as you can to take out the enemy as quickly as possible. Pounding away at them until the shield gives is something that reliably works. It may not work in time to save them, but what do they gain from NOT firing back? Rerouting power to shields is moderately pointless until they figure out why those're not doing their job, they had apparently no intention of getting out of there in a hurry so neither would rerouting power to engines (and the crew do usually mention it when they do stuff like that), so what did they have to lose? They either manage to take out the BoP so automatic win or they don't and still have to try the technobabble solution but have lost nothing by trying the traditional way.
Ironic since DS9 demonstrates this:
DS9 The Jem Hadar shows the USS Odyssey getting hammered by three Attack Ships which are able to penetrate the shields. The captain's response is to divert power from shields to weapons so they can do more damage. The Odyssey was destroyed in 2370 while the E-D went down in 2371.
Even then, the Odyssey is able to put up a much better fight than the poor old E-D and may have held out longer without the kamikaze.
That said, a single BOP was able to delay 10 Dominion Attack Ships off-screen in DS9: Once More Unto the Breach
This episode also shows a bit more creative use of the cloak with Martok raiding Dominion facilities behind enemy lines under cloak.
I think DS9 Rules of Engagement also shows a BOP and Cruiser being able to effectively tag team the Defiant to a stand-still. The cruiser you might get away with but a BOP should have no chance against the Defiant.
Overall, Picard openly mocks the idea of the BOP in Generations being able to take on the E-D. However, it would appear the BOPs are considerably more formidable than they appear.
The E-D really should have struck out harder than it did but it is possible the BOP would be able to withstand even the E-D going all out.