It absolutely is the case.
Not only do jobs gain access to more potent skills at higher levels, but they also gain more oGCDs to weave between their GCDs, increasing their APM ad overall DPS, plus they gain extra potency by way of traits like Main and Mend.
Taking Monk and it's AoE rotation as an example for DPS against 3 targets. And lets completely ignore Traits in this example as well, because I suppose you could say "don't sync traits"
Level 15: you have no AoE, your DPS is limited to your basic single target rotation. [Avg potency 206 per GCD]
Level 18: you gain a skill that gives you a 10% damage buff that should ideally be up constantly. [227 per GCD]
Level 26: your first AoE move [297]
Level 30: your second AoE move [341]
Level 35: you get an oGCD in Shoulder tackle that adds to your DPS [365]
Level 40: Fists of Fire, another permanent 10% damage buff [398]
Level 45: you final AoE skill [446]
Level 50: Perfect Balance (I'm not entirely sure how impactful this will be to the AoE rotation, but at the very least it gives an extra 30 potency each time you substitute Arm of the Destroyer, but I won't add this because it's not that big, maybe increases these numbers by 5?)
Level 56: Elixer Field, this oGCD makes a big difference. [526]
Level 68: Riddle of Fire, 25% buff that's up 22% of the time, slightly more than a permanent 5% damage buff. [548]
Level 70 + 74: Brotherhood and Enlightenment, I include these together because Brotherhood is what makes Enlightenment a reliable oGCD to use in the rotation. A little RNG here so this will have to be a rough guess, but typically you get to use it at least twice in each Brotherhood cycle so... [avg potency per GCD 579]
A level 15 Monk rotation is doing only a third of the potency of a level 80 Monk rotation, without taking any stat differences or traits into account. This could be exactly the same person, simply playing differently, using only their level 15 skills or their full level 80 kit.
(Also, this was using very rough 'per GCD' calculations, basically 'per 2.5-3 seconds'. If I were to do this properly and work out per second potencies, I'd also have to factor in Greased Lightning, which would create an even bigger disparity as it was skew it from ~3s to ~2s as more GL stacks become available)