We can always argue "It shouldn't be this way! Their tech should be better!" but that wouldn't account for the observed facts. It's IMHO only realistic to assume that several lines of technology and doctrine have been completely dropped when they lost in the rat race against their counterparts - and personal protection was among the losers, just like infantry armor and swords completely disappeared at one point in the real world, and only one of them made a comeback later on.
The only problem with that is Starfleet seems to suffer most of its casualties while dealing with people OTHER than Klingons/Romulans with modern shield-piercing weapons. We've seen redshirts taken down by spears, boomerangs, bullets, poison-dart flowers and explosive rocks; we've seen them cooked by radiation and beaten to death by apes. We've seen them thrown off of cliffs, electrocuted, impaled by shrapnel, accidentally beamed into deep space by their commanders... assuming you call these "combat deaths" that means Starfleet spends a lot more of its time engaging primitives or unpredictable elements than it does with people who would genuinely be able to penetrate their shields.
There should be no race to account for; some sort of basic protective gear should by now be as fundamental as shoes. Given the miniaturization of Trek power sources, it SHOULD be part of a standard field kit: phaser, tricorder, shield belt. Doesn't matter that the shield belt won't stop disruptors, photon grenades or psionic blasts from godlike beings, if it'll at least stop a BULLET, then that's a layer of comfort when your away team beams down onto a planet inhabited entirely by machinegun-wielding gangsters.