If the plants have everything they need to grow the tank will show zero ammonia and nitrite, and nitrate. Plants can do this well enough that bacteria would have noting available for the bacteria to grow.
Am afraid I have to disagree with a lot of what you mention here. The only way plants will show zero ammonia, nitrite and nitrate is if the tank is densely planted, I mean way more than the average newbie puts in their first tank, which is usually just a few plants to start with.
Also plants generally always have nitrfying bacteria on them and they do produce oxygen right down to their roots, this enables nitrfying bacteria to colonize. So that is a good arguement to have plants in the tank for cycling, though its certainly easily done without plants as well.
unfortunately changes in micronutrient levels can slow and even stop plant growth. Worst case the plants will even die. If that happens your fish would have to get through the resulting nitrite, and ammonia spikes without the aid of bacteria.
As mentioned, plants comes with nitrfying bacteria, and these bacterias will spread quickly on pretty much every surface int he tank as well as in the filter. the only case this spike will happen is if ALL the plants suddenly die and the tank is not cycled then there may be spikes in ammonia, nitrite and nitrate.
I would recommend cycling without plants and then once that is done put the plants in. This insures the bacteria will be there. The plants and bacteria would then work together to process nitrogen. If the plants for some reason stop growing The bacteria would quickly grow and process nitrogen.
If a normal fishless cycle is carried out without plants, and then add plants, its possible the plants can reduce the total ammonia in the tank that will then reduce the bacteria colony to the appropriate size to deal with what little NH3 is available.
Basically, the plants can cause the death of a certain amount of bacterial colony that was worked hard for to get during the fishless cycle....
Putting in the plants after cycling with ammonia is the safer way to set up the aquarium. Buying plant fertilizer may not solve the problem. Most fertilizers out there assume you will have at least some of the elements plants need. but occasionally tap water will be deficient in something. An if that happens you plants won't grow or grow slowly.
I have always maintained, and still do, that adding plants first, let the plants settle over two weeks or so, THEN start the fishless cycle.
This has several benefits, it can be quicker and more effective since plants comes with nitrfying bacteria so that starts the process immediately anyway. And with that, one can adjust the ammonia dosages accordingly so that works with any given plant load in the tank.
As for ferts, most fert companies assume that there is nothing else in the water, so they usually contain a certain amount of micro and macro ferts in balance. The only time this is really relevant is if starting a high tech planted set up with high lights and Co2.
The other thing one must consider is, if after a successful fishless cycle without plants and suddenly adding plants, how are these plants going to settle in properly before adding fish. There are many fish pick at or pull plants, disturb the substrate surrounding the plants and thus plants get uprooted etc so thats a consideration one must think of as well.
So to sum up, leaving the plants to settle in for say two weeks gives them a good chance to establish and grow some roots etc and then starting a fishless cycle and thus the plants are more likely to deal with whatever is thrown at them during the fishless cycle.
I have done this method with all my tanks without any issues at all tbh.