Two problems:
1. You're only measuring voltage with an oscilloscope. Or at best, voltage and current (using a simultaneous current probe). You could repeat the waveform, but if the surrounding circuit has a different voltage or current or impedance, the voltage and current won't match up, and the reproduction will be meaningless.
2. A much more reasonable substitute includes the impedance of the device. But evaluating this, in general, requires a great many measurements. It can be done -- there are frameworks for it -- but it's not easy, and almost never done as far as I know.
To continue the motor example, if it's at rest, and you apply a step change of 12V (from zero), then the current ramps up, peaks, then settles down. If you assume the device is linear (motors are actually pretty linear, for the most part), then you should be able to say, [emulated current surge] = [measured current surge] * (Vapplied / 12V), i.e., scale it linearly. But this misses a critical point: say we apply a step of 12V for a fraction of a second, say until just after the current peak; then reduce it to 6V. Does the waveform follow the same shape, just scaled instantaneously to the new voltage? No, it can't -- in fact you have to superimpose another waveform on top of the first one, this time scaled to -6V, to obtain the correct result.
And maybe 3. as well: the oscilloscope measurement is much noisier than the real thing, so at the very least you'll need to do some processing inbetween (filtering acquisition noise). Or maybe not noisy enough, depending on what kind of scope is used, and what acquisition settings. For example, a smooth ripple waveform won't replicate the high frequency "hash" of a noisy switching supply. And you probably won't have an SMU fast enough to reproduce a waveform like that, anyway.
No, testing is not done in this way; it's much too complicated to pull off reliably, and with a little cleverness, we can do just as well with simpler means.
For testing a power supply, we only want to know three things:
1. Is the output stable over its intended load range?
2. Is the output stable over its intended supply range?
3. Does the input or output have any quirky (voltage, current or time-dependent) behavior? If it is straightforward, then 1 and 2 are a sufficient description; if not, we should catalog the quirks (and, speaking as a designer, at least: we should try to fix them, as well).
Once these things are known, it doesn't matter what load we apply: we've already circumscribed all possible load conditions that any arbitrary load might get into!
Examples of quirks: a typical switching supply does not start up at low input voltages, and also delivers less maximum power at low voltages. That more-or-less circumscribes the range of input conditions. With respect to output conditions, the output voltage* is stable (within rated tolerance) at up to the rated current, then drops somewhere beyond there. The maximum power point may depend on supply voltage. Beyond the maximum power point, voltage drops rapidly, and the supply goes into a "hiccup" mode where output current periodically surges (as the supply attempts to restart, but can't because of the load). There may be a hysteresis curve, where when the output is "browned out", average output current is lower than the maximum output current.
*Or current, or whatever characteristic the supply has. We don't need to be exclusive of, say, LED supplies with a constant current characteristic. Or a dumb old linear supply, which will have a somewhat "squishy" (resistive) characteristic, say.
And that's about it. You wouldn't expect to see a sudden change in behavior as the input voltage changes from, say 110VAC to 130VAC, nor would you expect to see the output voltage start doing loops after tapping out an S-O-S in Morse code, in load current. (Which is entirely something you could program into a system, but that's going out of your way to make a system more complex than required, and why would you do that?...)
You may also want to do further reading on traditional tests: IEC 61000-4 series tests (in particular, ESD and surge, say), automotive load dump and other automotive voltage tests, stuff like that. The aim of these tests is to deliver a typical voltage, current and/or energy to the EUT. The stimulus represents a typical environmental hazard, of a typical rate, impedance and so on. Real ESD can be whatever voltage, but 15kV is on the high side even in dry climates, so it's pretty reliable in that sense, even if not testing the "maximum", whatever that might be in practice.
For these tests, it doesn't matter so much if the voltage, current or energy is delivered into the device, just that it survives exposure. For example, a well-insulated device will handle all the voltage, drawing no current and dissipating no energy. A well-shielded device will handle all the current, dropping (nearly) no voltage and dissipating little energy. A well-protected device will handle the voltage, current and energy.
The waveforms are important, because of electric and magnetic coupling effects. ESD is a very fast event, so it can couple into traces even within a PCB. Being able to test that, is a great help to improving reliability. Surge, on the other hand, is fairly slow, by an electronic perspective (~microseconds). Coupling isn't so serious here, but the magnitude of the event is (often 10s or 100s of joules, in that short period of time -- the energy of a bullet, in a fraction of the time it takes a bullet to strike!). And it's not always possible to open- or short-circuit a surge (because of other considerations -- mains voltage being the most common), leaving the only option to ride it through. Traditionally, MOVs are used for this purpose, and they can indeed stomach a lot of energy in a short period of time!
The surge waveform is affected by the method used to deal with it. Obviously, an open circuit draws no current. A clamped surge has a flat-topped waveform. A spark gap has a rapid voltage peak, followed by a flat clamping period. None of these can be -- or should be! -- simulated with a synthetic source. They're simply doing what they're supposed to be doing.

Tim