> exceeding the insulation rating
That's never the issue. "120V" windings use multiple layers of 500V insulation.
> the more load you put on them, the hotter they get
True, but still not the issue.
Vacuum (or air) carries magnetic flux with a factor of "1". Good transformer iron carries magnetic flux with a factor near 1,000..... up to a point. (Actually its permeability changes with applied magnetic force.)
So as you raise voltage on a "120V" winding from 10V to 120V, 99.8% to 99.9% of the flux passes through the iron, causes self-inductance, opposes the applied voltage. The no-load current is small.
This is true up to about 5,000 Gauss in the iron. But at higher Gauss, "all" the iron molecules are magnetized and lined-up. The iron is "filled up", it "can't hold any more".
Now when you raise voltage more, past 120V or 130V or whatever safety-margin the transformer winder put in, the excess voltage and excess flux "spills out". Self-inductance falls very low. The no-load current rises very high.
If you ask around your Electrician friends you may find one who saw a 240V winding on a 440V feed (oops!). At best, the fuse kept blowing right after switch-on. But in bigger systems it can heat and burn.
If you have a fire-proof bench and lots of excess transformers, you can try it. Plug a 120V winding to a 120V outlet. It idles nice, slightly warm. Now plug the 120V winding into a full-power 240V outlet. It will pull a BIG current, hum loudly, blow fuses or smoke and burn.
If you have a high-power Variac, and a way to measure AC Amps, you can plot it. No-load current is small 10V to 120V, rising at 130V, and rising fast at 150V.
That excess no-load current causes I^2R losses and heat in the winding. So for a "little" over-voltage, and a little excess heat, you can de-rate the transformer for lower VA output and less load-loss heat. But at some over-voltage the no-load current alone will quickly over-heat the winding.
> can I use a bigger first transformer and a smaller second transformer ?
Yes. In fact since in most tube amps the heater power is as-big or bigger than the plate(s) power, the second transformer can usually be half the size.