Non-canon speculation: The modular design of the Galaxy Class ship allowed the ship to be configured for many different situations. The first ship assembled was configured to accept a secondary warp-reactor. It was intended to be used during the early flight-tests in the event the primary warp core developed issues during high-energy regime testing modes. The second, third and fourth units retained the ability to install a secondary reactor, however only the USS Enterprise was actually fitted with one. It was decided due to the Farpoint Mission profile a secondary "return home" capability was needed as the ship would be exploring far beyond the Federation boundary.
When the Farpoint Mission was canceled (due to the loss of the staging base) the Enterprise had its secondary reactor removed at a Starbase layover. It was decided that the increase in vehicular mass and system redundancy outwayed the safety margin provided. Given the Enterprise's new mission profile (never more than a few weeks beyond Federation space) the reactor became an unneeded piece of dead weight.
Block Two and Block Three Galaxy Class ships (Dominion War Ready-Frame Buildup Units and Post Dominion War New Build Units do not retain the ability to mount a reactor in this location, instead the secondary warp reactor install point was moved to the saucer section to provide a power source for potential future saucer warp-drive installations.