Can also be troublesome just to even trigger on a given signal, when there are multiple frequencies in play; when this happens, a local probe probably helps (trigger on the source you're looking for), then averaging on the trace (DSO FTW).
Would you need to trigger? Couldn't you just acquire a few mega samples of data and run FFT on that? Of course this doesn't solve the dynamic range issues.
But that just tells you what the spec already tells you; which is nothing about how they're correlated in time. Usually you'll have (semi-)periodic signals in the circuit, and you can look at each, e.g. SMPS switch node, or CPU clock (if they differ), to tell which is which. But if they have similar amplitudes at the point of measurement (e.g. probing a cable or LISN), you can't trigger on one or the other, you get both. Sometimes the amplitudes differ enough to catch just the taller one, but if you're trying to track the smaller one, that's no good.
Put another way: you see some peaks on the spectrum. How do you correlate those with some impulsive noise in the circuit, and ultimately to an offender?
And, say, placing a finger on the offending switch node, ought to pull enough common-mode current to raise the respective peaks on the spec (assuming the switch node is safe to handle..!), so you can figure it out in that case, without having to track through a scope. But that might also be hard to do (say with everything buttoned up), but say you've got access to some related signals, that might be a use case for the scope.
...Oh, and about nonperiodic stuff; if you can trigger on it and see that that's the offending problem at the LISN or whatever, that helps, too. Spread spectrum, or variable-frequency (e.g. QR flyback, LLC) converters, the spectrum is just a blur, easy to hide many overlapping sources within. Scope can help you separate those too.
During radiated / conducted emissions tests average or quasy-peek measurements are used. So a pulsating / sporadic signal won't cause much trouble to pass EMC testing; the continuous tones (or frequency bands with continuous emissions) are the problem to pass EMC. There isn't much to trigger on.
So no one's ever had an SMPS fail radiated (>30MHz)?
Trouble is, impulsive noise also tends to have high peak amplitudes. A 400V switch edge, even with considerable attenuation, can still be say 10s of mV peak on the outside, and QP won't quite save you enough to pass.
Tim