It's an interesting premise to think of the deactivated "antimatter fuel system" in the warp drive pods to have vented out their supply.
Assuming that the front of the TOS starship nacelles contained the matter-antimatter reactors (those of the Constellation had been destroyed), there'd be indeed little reason to keep antimatter supplies in the warp nacelles as these would only constitute an unnecessary hazard.
But what about the antimatter not in the warp drive pods? There is the antimatter fuel in the engineering hull ("That Which Survives") and also possibly the antimatter fuel on Deck 11 in "Errand of Mercy" to consider.
Could be a useful hint that the Constellation belonged to the Constitution Starship Class (NCC-16XX) and only the Enterprise Starship Class (NCC-17XX) featured another M/AM reactor in the engineering hull and the antimatter pods on Deck 11.

BTW, I do agree that the antimatter fuel is generated as needed instead of giant fuel containers as portrayed in later Trek.
I most certainly don't. The amount of energy you need to put into the creation of antimatter equals the amount of energy yield you could get from matter-antimatter annihilation ("You canna change the laws of physics").
These enigmatic antimatter generators look like "magic".
On the other hand, if those large deuterium tanks (e.g. NCC-1701-D) were antimatter tanks I believe it might be easier to rationalize that space energy and/or matter is collected during flight. Hydrogen particles are available in open space, antimatter is not.
I would find it much easier to assume that warping space requires less M/AM annihilation than assumed. However, matter and antimatter tanks should have a more or less equal volume to credibly illustrate the 1:1 annihilation ratio.
Bob