You can't really have a full medical staff of holograms (even for emergencies) as they take up a lot of space in the computer core
That was only problem with the Voyager
holodoctor, who was allowed to grow unhindered. Holographic nurses could be extremely simple programs compared with holographic entertainment characters, yet very useful in an emergency.
As for replicating medical instrumentation quickly, a Cardassian food replicator quickly produced a working phaser that immediately started firing in "Civil Defense". This shouldn't be a bottleneck as such, then. It's more a question of how much you want to rely on equipment and facilities generated on demand in a combat situation where your generation abilities may be compromised. And it shouldn't be difficult to simply keep equipment in stock; the holodeck-simulated sickbay crashing in the middle of a situation might not be all that fatal a failure, either, provided the patients are at least held on physical beds or stretchers rather than flickering forcefields.
Seems to me it would be easier to have the EMH control any holo nurses directly with his own program, them being only the physical versions acting as he wants through a computer link or something. That'd speed things up as the "nurse" would be on the same page without them having to even talk.