Alright, so I admit I read the first five posts then skimmed the rest of this thread, so if this has already been said, I apologize.
Although I do have a hobby oscilloscope, and love using it, to be honest at least 90% of the measurements I make with it are very basic, and could be handled by simpler equipment such as a frequency counter, power meter or peak detector.
I mean, think about it. The majority of (steady state) signals are going to be known to some degree, i.e. not completely random and unknown in characteristics. How do you characterize an *ideal* pure signal? By it's frequency and amplitude, and as a distant third, by it's phase offset from some reference signal of equal frequency, if this is relevant to the situation.
How do you characterize real (non-ideal) signals? With the same parameters, plus various measures of their "non-idealness" such as phase noise, spurs, % modulation, frequency deviation, etc. depending on the signal type and circumstance. While a spectrum analyzer may help tremendously in this type of characterization (and I'd love to have one myself), many of these measurements can be made with simpler equipment and some knowledge of the nature of your signal and system under test.
Honestly, while I love making measurements on my scope, I often don't really need to see a time domain image of the signal, more just use the scope for measuring various properties of the signal of interest, such as period or frequency, amplitude, number of cycles in a burst, DC offset, etc. Of course there's many things a modern scope is useful for, such as rise time measurements and close inspection of pulses and things of that nature, but the *majority* of signal viewing (for me) is just a side effect of trying to measure the basic properties.