That original statement is actually quite accurate. White Mages typically only have very few "offensive" spells, and they're sometimes only effective against undead.
FF1 - They have "Harm" spells that only affect undead enemies, and then all of *one* non-undead specific spell (Holy), which is at the highest tier meaning it's learned very late in the game and you have very limited uses of it. Try having your White Mage use anything else for DPS (e.g. physical attacks), and it's pitiful.
FF2 - Holy and Ultima are the only offensive spells, with Holy being the most expensive white magic spell (and 2nd most expensive spell overall) and Ultima learned from a special book, again both well into the game.
FF3 - Finally we get *one* damaging spell that has upgrades over time (the Aero series), and the usual top-tier, late-game "Holy" spell. In other words, for almost the entire game, if your white mage is doing any DPS, they're spamming one spell over and over (sound familiar?).
FF4 - We're back to losing even that Aero-line. The *only* offensive spell for White Mages is Holy, and as usual, it's the last spell White Mages learn (at a high level late in the game) and costs a lot of MP.
FF5 - Same as FF4. Holy is the *only* offensive spell for the White Mage job.
FF6 - This game used a different system entirely, where you could give any character any combination of magic you wanted through Espers, so there wasn't any actual "white mage" class.
FF7 - This game did something similar, but with materia instead of espers.
FF8 - This likewise had the junction system without a clear "white mage" class.
FF9 - Closest return to white mages, with certain characters having "white magic" abilities. Holy is once again the *only* offensive spell.
So, I'm sorry, but the original poster is *completely* correct. White mages in FF1-9 have very little in the way of damaging spells. In most games, they only have *one* offensive spell, period (and it's not learned until late in the game and costs a lot of MP to use). In FF1, they have an added spell line that only works against undead. In FF3, they have one added spell line that works against anyone, meaning you can spam the same single spell. In all of these games, trying to do physical DPS with a white mage is pointless. FF as a series has never promoted white mages DPS'ing. They best they did was effectively abandon classes altogether and let anyone have any combination of spells they wanted, but by that point the concept of "white mage" itself was gone.