We might argue that the E-D never had a Captain's Yacht. After all, the backstage material (TNG Tech Manual, Andrew Probert's artwork) indicates that such a yacht would be mounted at the bottom of the saucer, but "Encounter at Farpoint" establishes that the E-D has some sort of an energy beam there instead.
Perhaps the
Yamato and the
Odyssey had Captain's Yachts for missions of diplomatic representation, but the
Enterprise was completely dedicated to such missions herself and didn't need to carry a separate craft for the function... Other
Galaxy and
Nebula ships may have carried other types of equipment in that saucer-bottom berth, ranging from gun turrets to special sensors to deployable laboratories etc.
I know a story-related reason has since been created saying Voyager was launched before its aeroshuttle could have been installed
The ship did sail out rather hastily, apparently, so this rationalization would make quite a bit of sense.
OTOH, the thing dangling below
Voyager was never really supposed to be a Captain's Yacht, not in the same sense as the E-D craft. The TNG Tech Man describes the Captain's Yacth as a luxurious interplanetary/atmospheric vehicle, essentially a flying office or embassy; the VOY equivalent was described as having warp capability and utilitarian features. Of course, the E-E saucer-bottom auxiliary also had warp capability and utilitarian features, including austere interiors... And was canonically referred to as the Captain's Yacht in dialogue.
Timo Saloniemi