I want to add, that the sheer volume and size of the saucer section might be the reason it has no warp drive.
To generate a warp field (big enough to transport that mass) the whole warp system woud certainly have to have a drive, comparable to that of the battle section. That means less space on the saucer for labs asf.
So, actually, it could be easier to generate a warp field around a smaller object - because it's mass-dependant.
...And remember, that the warp nacelles (almost?) always reflect the size of the the ship to carry?!