Probably Starfleet relies on a range of survival devices that may include "almost-shuttlecraft" with a high degree of independence and maneuverability, "dumb" pods that merely float in space until recovered by a suitably equipped starship, and "even dumber" survival cocoons that are just flimsy balloons containing an air recycling device and one to ten survivors.
The bigger and better survival devices might need to be housed in a shuttlebay, although probably not the same way shuttles are housed: the pod that saved Sisko could have been hanging from the ceiling of the shuttlebay, for example, until called to perform its one-off duty, thereby not unduly hindering normal shuttle operations. Simpler devices might need less maintenance and could be stored near-indefinitely in their designated, isolated berths in seldom-visited parts of the ship.
What is housed behind those hatches on TNG era ships is probably not set in stone: some ships may have a full set of the latest model of survival pod, while others may carry a mixture of older and newer pods there, and some pod types may be much smaller than the hatch they're hiding under. The Voyager
pods clearly defy stereotype by being small hexagons beneath "standard" large square hatches. So I think any portrayal of Wolf 359 evacuation would be fully justified in featuring a broad range of devices and designs.
OTOH, how many ships really had the chance to launch survival devices? The Saratoga
was caught in a tractor beam for a couple of minutes, but when Sisko launched out of that doomed ship, half a dozen starships outside were burning wrecks already. The Borg might only have allowed a select few ships to survive long enough for their crews to attempt evacuation.
And if their goal indeed was to improve the quality of life of their victims, they'd be unlikely to miss the opportunity to capture all the escape pods they could, and convert the occupants to a blessed existence as Borg Drones.