The input capacitance of any input should be a dead giveaway that a derating of the overload limits will be needed. There are at least two cases:
The input attenuators (frequency compensated voltage dividers) are unlikely to require a derating. The voltages remain constant, just the input current rises proportional to the frequency. Yet this could become a problem in certain situations.
Consider 100 W / 50 ohms / 140 MHz -> about 70Vrms @ 140 MHz. With an input capacitance of e.g. 16 pF this is a reactive load of 70 ohms at 140 MHz. The reactive peak input current will reach 1.4 A! This could easily be a problem, e.g. for the signal relay that is switching the attenuator.
In general, “power dissipation in a capacitor” should never be a problem here. Not for the DC-blocking as well as the frequency compensation capacitors in an oscilloscope frontend. These have high quality dielectrics with negligible loss (ESR) – we’re not talking about electrolytics here.
Then there is the input buffer. The LF-path is high voltage tolerant with lots of (protective) series resistance (and high noise). The transition to the HF-path is 6 dB/octave and starts at a frequency between some 100 Hz and some kHz, depending on the design. The principle is pretty much the same for any modern general-purpose oscilloscope, i.e. the ones that provide a high impedance input of 1 MOhm // something.
The HF-path has no series impedances other than a small capacitor, whose impedance is essentially zero at high frequencies. This is why we can have high sensitivity and low noise down to about 3 nV / sqrt(Hz) at frequencies above several MHz, but certainly no protection anymore, apart from some clamping diodes. The latter are already a problem even at moderate frequencies below 1 GHz, because they add a voltage dependent input capacitance, which, among other things, means distortion. So we want to use the fastest diodes (or transistors) with the best HF features and lowest junction capacitances. It just so happens that such components cannot handle high currents. Consequently, such a clamp easily fails and the following HF buffer could get fried by any substantial overload.
A proper DSO will activate two cascaded attenuators to provide the maximum attenuation for 10 V/div, only one attenuator for 1 V/div and no attenuator at all for 100 mV/div and lower. Cheap DSOs make do with just one attenuator in total.
Now consider 70 Vrms = 200 Vpp. If you are a bit sloppy and accidentally switch the scope to a vertical gain of 100 mV/div or below, so that the input attenuators aren’t activated, then the full 200 Vpp reach the input of the HF-buffer via the DC blocking capacitor that might be something like 1 nF.
Even at very low frequencies like 3.5 MHz, the reactance of a 1 nF capacitor is only 45 ohms! Now consider what (for example) the sensitive dual gate MOSFET and the fragile BAV99 clamping diodes in an average low cost HF buffer will have to say when they need to face a 200 Vpp signal from a low source impedance – even if it is applied only for a very short time.
As we are at it: a x1 Probe is not nearly the same as a direct coax connection. The latter requires a proper termination for meaningful results at higher frequencies. The x1 probe needs no termination but has a very limited bandwidth of usually less than 10 MHz from the outset. Everyone can use an ohmmeter to measure the resistance from the probe tip to the center pin of the BNC connector – does this look like an equivalent of a direct coax connection?
EDIT: false assertion about signal handling capability above 1V/div deleted.
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