Who does it seem that all the Starfleet ships we've seen, with the exception of the 1701 in TWoK, have vertical Warp Cores? On the Enterprise D it seemed to take up 2 decks, but specs, as I recall, showed it at 4 decks high. That's some 40 - 50 feet if you assume those decks it transverses have Jefferies tubes. Geordi almost fell from one of those decks and, if I again recall correctly people have been seen dangling from the platforms while the ship is in battle due the shaking of the ship.
Wouldn't a horizontal Warp core make a bit more sense? No decks to climb and the chief engineer or specialist can run to the area of the core that causing trouble. And whether it's laid vertically or standing horizontally it'll still take up room making Engineering one of the biggest rooms on the ship. But at least laid out it's easier to get to all the parts.
Granted, it may have to be lifted 4 or so feet off the floor to allow access to its under belly, but that's still safer than reaching across a ledge.
Please give an in universe explanation, before a filming standpoint. Two filming standpoint I see right off the bat is that you get to see the pretty pulsing or swirling lights and more of the core when it's standing up.