I'll accept that the fighter was the most popular class during this period (I have no reason to doubt it), but granting that, it was the most popular class among players who didn't simply quit the game for a different game/edition or skip it entirely.
Yep. The popularity of the fighter transcends edition. Long-time players still like the fighter. Brand-new players gravitate to the fighter. Fans of 3e liked the Tier-5 fighter. Fans of 4e liked the balanced Fighter-as-'defender.' Fans of 1e liked the castle-building 'Lord' Fighter. Fans of 2e liked the TWF/double-specialized Cuisinart-of-doom fighter.
I have no idea if it was still the most popular class in PF (IIRC, PF did beef the class up substantially, didn't it? CMB, alone, seemed to me a boon), so I wouldn't be at all surprised if it were. Paizo ever run a class-popularity survey?
(Disclaimer: I skipped that edition because I was on hiatus when it launched, and I therefore missed all the edition warring, too. My sense of what happened is cobbled together after the fact.)
You're not wildly far off. There was a very strong initial reaction against the wizard & fighter in 4e - and to the absence of the Gnome from the Player's Handbook. The former was "nerfed into the ground," the latter was "casting spells." While the wizard was orders of magnitude less versatile/powerful than the "Tier 1 godwizard" of 3.5, it was still hands-down, the most versatile class in the game, with the unique ability to swap out spells on a long rest (something other classes eventually poached in a much more limited way at the cost of a feat per alternate power), at-will utility cantrips and non-combat rituals. The fighter, OTOH, categorically did not cast spells (and absolutely does cast spells in 5e), so that was prettymuch just blowing smoke. The Gnome appeared w/in a year, in the PH2. Hostilities escalated and made-up terms and recriminations flew, but it was, at bottom, mainly about the balance between 'martial' characters, particularly the Fighter (& Warlord), and casters, particularly the Wizard.
Essentials obliged, giving the wizard more powerful spells, increasing the power of many existing spells, & granting it still more flexibility to swap more of them out, and stripping the fighter of virtually all its maneuvers.
It wasn't enough.
5e was enough.
But none of that was enough to blunt the popularity of the fighter.