So what you're saying is... weapon strength improved SIGNIFICANTLY between TOS and TNG!
Uh, no. I was pretty clear about what I said. However, let's go with YOUR "theory". If what you say is true, then the Federation REALLY fell behind in the offensive/defensive curve because THEIR weapons had less of an effect on most of their opponents during the TNG era, as opposed to the overwhelming effectiveness that their opponents weapons had over THEM. Almost everyone was slapping the Ent-D around, from junkyard BOPs ("Rascals"), to a 20 year old BOP ("Generations"), to a minor race like the Tamarians ("Darmok"), to the Romulans ("Tin Man"), etc. It's painfully clear that in "Rascals" and "Darmok" that those ships were inflicting WAY more damage on the Ent-D, than the Ent-D was inflicting on THEM. The sad thing is, in both of those examples, it was clear that within the first 5 seconds of the battle, that the Ent-D was in SERIOUS trouble.
Even in "Generations", the Ent-D weapons couldn't penetrate that old BOP's shields, as evidenced by the Klingon tac officer's statement that "Our shield are holding". Holding against WHAT? That statement has NEVER been uttered in ANY Star Trek unless something was impacting against someone's shields, so it's clear that the Ent-D was still firing on that BOP even though we didn't see it, but their weapons were so ineffective that it could even whittle down that much smaller OLD ship's shields down. Sadly, we see the same kind of weapons ineffectiveness from the Ent-D sister ship in "The Jem'Hadar". Even with their shield power transferred to their weapons, they were completely useless at destroying a single Jem'Hadar ship.
So if these lackluster results are considered as "weapon strength improved SIGNIFICANTLY between TOS and TNG", then it's no wonder that the Federation needed Section 31 to assist in the security/defense of the Federation, since their TNG era ships clearly was not up to the task.