Time and frequency are the same thing. If a DAC can reproduce 20kHz at full output, then it is fast enough to reproduce all audible transients. (20kHz, after all, is 20,000 cycles per second.)
If a cymbal hit has a risetime faster than 20,000 cycles per second (which is absolutely plausible, as you say), all that means is that it produces some frequencies that humans can't hear. If we can't hear these frequencies, we don't lose anything when they are absent. The cymbal sounds the same whether or not those frequencies are captured/reproduced (and btw, they are rarely even captured in the first place).
You appear to be correct. The ''fast transition'' hypothesis states that when you go from say 20 Hz o 20 kHz, some DACs might struggle with the transition, which doesn't make much sense if you can reproduce 20 kHz continuously. If you can reproduce 20 kHz, it shouldn't matter ''how'' that 20kHz is arrived at.
It's not like a car where accelerating from 20 to 200 mph is obviously different than accelerating from 190 mph to 200 mph. The first clearly takes a lot more time than the second.
With frequency, it's different. If you want to reproduce 20 000 Hz, you don't get any ''help'' from starting at say 19 000 Hz. It's the same thing as starting at 20 Hz, or dead silence for that matter.
You can easily visualize this.
Imagine a graph of a continuous 20 000 Hz sine wave. Pick any point on this graph where the wave intersects the X axis and mark it.
Next, imagine a second graph, of a wave which changes frequency from say 5 Hz to 20 000 Hz at some point which lies on the X axis. Mark this point also.
Now compare the portions of the two graphs beginning at the points you marked. Both are identical - constant 20 000 kHz, starting at zero. What came before doesn't matter in the least.
In other words.
Case 1. Take a car and accelerate it to 200 mph and brake to a standstill a bunch of times, and then, from standstill, accelerate to 200 mph again.
Case 2. Take a car and accelerate it to 5 mph and brake to a standstill a bunch of times. Now accelerate to 200 mph from standstill.
Do you think the result of the final acceleration from standstill to 200 mph will be any different between the two cases?
My illustration should make this easier to understand, if you can forgive my terrible handwriting skills.