An Emergency Tactical Hologram force will cost more energy than more effective defenses
In the Voyager episode The Killing Game, we see the entirety of Voyager being refitted with hologram emitters in order to turn the ship into one huge holodeck, running hundreds of characters over tens of simulations.
At this point, however, Harry Kim is already complaining to the Hirogen that the holodeck systems are being absolutely overloaded, and he's told to "make it work." To be fair, he does get it to work, but it's taking all the computer and power resources on the ship.
A ship under attack from the Borg will not likely have the open computer time and power to run an army of hologrammatic soldiers
Holograms themselves require a ton of data processing to work well; according to the Starfleet Technical Manual, the Holodeck basically has its own computer core... subprocessors dedicated to hologram simulation. In order for The Killing Game to work, the programs were still running on the Holodecks, but distributed over the ship. This requires gigaquads of data roundtrip to the transmitters; static images are easy, but Emergency Tactical Holograms would require much more interaction... and again, a ship currently under Borg attack won't have the CPU to spare.
Your regular, run of the mill holodeck characters wouldn't have the tactical ability to be effective in combat, especially against an enemy who learns from interaction
The Hirogen went through all the trouble of adding the Voyager crew to the holodeck not out of sympathy or convenience, but out of necessity. As the best hunters in the galaxy, they quickly found holodeck characters to be extremely pointless. They were never able to "match" the Hirogen in battle abilities; as such the Borg would (with their Hirogen assimilations) be able to easily go around the holodeck characters.
It's possible to make Emergency Tactical Holograms that are good fighters... but the Federation would refuse to do that on moral grounds
The Hirogen do exactly this in Flesh and Blood. They create self-aware intelligent holograms because "it wouldn't be interesting otherwise." And these holograms ARE able to fight back well, and end up massacring the Hirogen; the holograms die and die over and over again, learning from each excrutiating death.
The Federation won't condone creating artificial intelligences simply designed as cannon fodder. At least a Redshirt who enlists makes the intentional decision to join Starfleet; what do you do with an ETH who decides to take up Parrises squares? ETHs would need to have an analog to fear, as fear can be useful in designing tactics and pushing through obstacles... but is it ethical to program a lifeform to be terrified, and force them into combat anyway?
The only "forced duty" holograms we know of are the EMH-Mark-1s from Author, Author. At the end you see tens of EMHs working in a mining colony, and you get the implication that it's "forced labor." But considering the massive energy and CPU requirements to run so many copies of the EHM, I see something else: a group of lifeforms doing work to pay their own way. Somebody has to supply the energy and CPU time; in exchange, the EMHs mine and get to experience holonovels in their off-time.
Why would this be? Because Starfleet discovered that EMH-Mark-1s (and probably 2s) emerge through "well-programmed character" to "actual sentient life form" and they can't just "kill off" all the old holograms, they have to go somewhere; they can't be stored to disk forever, Moriarty didn't handle that well. Something's gotta pay for the multiple warp cores, holo-emitters, and computer time necessary to keep a colony of EHMs running...
Basically, Long Story Short: ETHs provide no benefit that other tech can't provide for cheaper
Build anti-nanoprobe-nanoprobes. Have a computer program that roves security shields as security teams run through. Use the transporter to beam grenades into their squads. Put phaser strips in the corridors so the ship can literally shoot back. Just about any of these ideas are more power- and CPU-efficient than ETHs.
