You are welcome, U-V2.
About Q/A1: I am unable to give answers; I believe this is one for Sergey, @Sergey Osokin
About Q/A2: The (perceived) smoothness as it appears on screen depends on the monitor; it can be influenced by artificial means inspired by PS, however adding a raster effect to the gradient, which I believe may more or less be the way used in Blender.
In connexion with printing, the smoothnes/lack of banding/whatever depends on the actual printer, including whether it is working with PostScript (emulation) or printing from Acrobat based on a PDF; the actual print is the proof of the pudding.
"I'd like to know if you have a good method for "making gradients as soft as possible" if you're willing to do so."
As mentioned above, "But it is actually possible to get a soft and even transition in Ai by simple changes to the default values used in the inherent gradient (only the actual transition shown below)."
However, I am afraid it is impossible to fulfil this, automatically being the key word:
"What I need is a fully automated method that, when I enter the color values of all the necessary colors, automatically generates a gradient with a perfect transition that doesn't look out of place on the printed product."
Ai allows for wide ranges of options, but at the cost of customization/adaptation in the workflow.
"I'd like to know if you have a good method for "making gradients as soft as possible" if you're willing to do so.
Also, if this method involves manually inserting a transition color between two colors, then this method will definitely not work for me."
The gradients shown are based on the same 6 regularly spaced stops (RGB: 255/0/0, 255/255/0, 0/255/0, 0/255/255, 0/0/255, 255/0/255) as in your Blender sample, only starting at 0% and ending at 100% (transition throughout), and with no Color Stops inserted in between (beneath the Gradient Annotator, see link).
But the upper gradient has all Mid Points (beneath the Gradient Annotator, see link) at the default 50%, whereas the lower smoother gradient have the Mid Points moved to 33% and 67%, closest to the R,G, and B (RGB: 255/0/0, 0/255/0, 0/0/255).
You can try it out and decide whether such (limited) customization/adaptation is bearable and relevant in your workflow; this way can be fine tuned to get the smoothest/most pleasant transition in each case.
I believe it may be possible to make it easier by script or action.
https://helpx.adobe.com/illustrator/using/gradients.html
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