I find it rather bizarre that Adobe has, in effect, just designed autotone to work just with Adobe profiles and I support Andrew's request to "uncripple" this "feature".
Actually, if you understood what went into training the AI you would understand that the ONLY profile it makes sense to use for Auto is Adobe Standard (or Adobe Color which is Adobe Standard under the hood). If you think about it, Adobe would need to train the AI on each profile included with Lightroom which just ain't gonna happen. The profile is the basis of the tone curve that the AI uses to evaluate and tone map the image. Change the profile you are forced to change the tone mapping.
I do think Adobe should pop a warning when applying Auto to new images whose profiles are NOT at Adobe Standard and offer to change the profile to Adobe Standard but I suspect that won't happen either...
The reason I know so much is I've been working with Adobe since last year trying to train the AI on what images should look like. I've adjusted 1K of my own images and 1,500 images from other photographers from all sorts of cameras and scenes. The AI still messes up from time to time but the vast majority of the time the AI moves in the right direction even if it does a bit too much (or not enough) of certain adjustments. I'm due to adjust another 500 images by the end of the month. These are weird edge case images to train the AI on unusual images.
Personally, I now auto tone all my new images at import because it makes selection editing so much easier...and since the AI is already trained on my style and taste, the AI is usually pretty accurate.
The only limitation is, of course, the AI can ONLY do global adjustments, no local adjustments (although that might show up in the future).
So, if you like the way Auto works, you can credit me...if you don't like the way it works, blame Adobe :~)