The fundamental limit is 1. the maximum length of wire used on any winding, and 2. how closely spaced that wire is, relative to the circuit impedance the winding terminates into.
It's a matter of impedance matching, just as you would with transmission lines; but without needing to consider geometry (windings can be quite complicated, so a wave of the hand will suffice), and the 1st order lumped equivalent (RLC) will do.
Or put another way, a transformer is just another kind of transmission line or filter, and so its frequency response and impedance are characteristic.
So, #2 has quite clear limits, because even for very loosely spaced wires, the characteristic impedance is 100s of ohms, while we might need 10s or 100s of kohms for a HV supply. A stack of layers can have this over and over again, so that the impedance between adjacent layers is 100s of ohms, but the total stack is kohms. But this comes with a significant penalty in frequency.
A stack of stack of layers (the bank winding Dave mentioned) can limit the amount of frequency penalty to a per-section basis, again keeping turns or inductance high while keeping the frequency limit more manageable than a single solid block winding. But still, you probably aren't going to get, say, 10s kohms or 100s mH in the low MHz.
So we inevitably must deal with limited bandwidth and impedance mismatch. Impedance mismatch manifests as a peaked, bandpass response. Just what you'd want for a resonant supply anyway, and impossible to push a square wave through, hence standard switching supply topologies aren't so great here, and resonant is the usual approach.
There are some strategies that can extend bandwidth. If the secondary can be made in a single layer, it can be limited only by the frequency response of that solenoid. Even with a wide winding bobbin and very fine wire, we might only manage a few kV this way (and a cutoff of a few MHz). But, suppose we add a diode and capacitor to this one winding, making a DC supply; then stacking another on top, and so on. If we align the secondaries of these supplies, so that they all start and end at the same sides, and all have the same number of turns in their single layers, then we actually get no AC voltage between layers -- they all track each other like a single thicker winding. They act in parallel at AC. But each one stacks on the previous at DC, so the capacitance between layers acts as filter capacitance.
Do this over, a half a dozen times or so, and we get what's in a typical CRT flyback transformer. These offered bandwidth up to the low MHz, with a high voltage output of 30kV or more! They were operated quasi-resonant: the switch is on for a relatively long time (most of a scan line, also being coupled to the deflection coil to do that at the same time), then in the about 10-20% remaining during horizontal retrace, the switch turns off, and the transformer goes through a resonant cycle or two.
I'm not sure if the fastest multisync monitors used combined HV and deflection (I know some Trinitrons didn't; they had a separate HV supply, with a MOSFET switch, independent of the deflection supply with a rather beefy BJT), but a lot of mid-tier monitors in the 1280x1024 sort of range (while still supporting resolutions down to 320x200) did this. Probably the transformer wasn't allowed whole cycles of ringdown in some of these scan rates, but supply voltage and timing were adjustable by the controller to compensate.
This is really just reiterating a lot of things I've already said, but maybe the relationships and proportions will be more apparent this way.
Tim