The theory is OK but the practicality of using a relay makes that idea unusable. Assuming your frequency sweep is fast enough to appear continuous, the relay would have to switch at twice that speed. You are probably looking at switching at least 20 times per second and the switchover has to be synchronized to the sweep. The same speed is needed for amplitude switching, essentially you are swapping between the normal display and a reference display at sweep frequency.
You could possibly do it with a semiconductor switch but then you would have to be careful with bandwidth and voltage capabilities, especially at GHz frequencies.
If you can get access to the intensity control, a better solution would be to brighten up a spot on the trace and from the horizontal position, calculate the frequency and simultaneously "sample and hold" a snapshot of the amplitude. It requires some circuitry but the sweep waveform is already available and measuring a voltage will be more accurate than visually aligning two alternating sweeps.
Brian.
That last paragraph, reminds me of an old Tek SA where they introduced a notch at a movable point on the screen, then measured the frequency of the notch with a mehanical meter.
Why do I have to switch the relay that fast?
Actually, there will be no automatic switching at all, but a user switch (eg with a button). The user will switch the two waveforms up to the point where their amplitudes/frequencies are the same. The eye can easily track the positions of the waveforms that appeared on the screen a few ms ago and have now vanished and replaced by the other waveform.
In the Tek 491, which has a P7 phosphor with high persistance, this is even easier. In fact these oldies were based on persistance as a form of analogue "video memory", so as to operate the sweep oscillator at a lower rate and achieve higher resolution, yet draw a usable line onto the screen.
But the same idea can be usable in screens without long persistence because of the eye/brain persistence of vision. It is actually easier than it sounds. For example when you see two dots of alternatively switched laser pointers, you can easily bring them at the same position.
With this idea, you avoid all the hassle of interfering with the internal circuits of the scopes/SAs and it is more universal, although not really accurate like you said, but yet quite usable, far more than counting squares.