You know what's interesting? Both the Defiant and the TMP Enterprise had their phasers fed directly by the warp core, and both (+ the Reliant, maybe all TMP era ships) had pulse phasers (or "pulse-ish" in the case of the TMP ships).
Although we didn't see the Enterprise fire her phasers in TMP and by TWOK they were different again. But as I said, maybe the charging function was added again as a backup.
Or, the TMP phasers were an experiment to increase their power output that didn't work well (maybe because it was still too dangerous to have high energy warp plasma circulate though the whole ship), so by TWOK, the ships were outfitted with the old TOS energy distribution network again and the "pulse phasers" were developed, which utilized the old TOS charging mechanism again but were stronger because the pulsed discharge dealt additional explosive damage to the target.
By DS9 then, on the Defiant, the direct warp energy supply to the phasers worked and was also combined with the stronger pulse phasers.