You mentioned that the stops are identical, but then you said that the phone photos are noisier at the same ISO. You didn't mention this, but there will also be a deeper focus plane. So they aren't identical -- at least under the sense of the word "identical" that's useful to me. You need to use a much slower shutter to get the same noise level. Or a much faster aperture at the same shutter speed.
That difference is exactly what I'm talking about. You'll generally find that a cell phone photo has about the same noise once if you divide the ISO by the square of the relative crop factor (and set exposure accordingly). Coincidentally, you also need to use an aperture that's faster by the relative crop factor to get the same level of background blur.
I never claimed taking photos on a minuscule sensor with a plastic lens is identical to doing so with a high end DSLR. Stops refer to exposure and noise and depth of field have no bearing on a photo's correct exposure. It seemed to me that parent was spreading a common misconception about how exposure works across different sensor sizes so I wanted to correct/clarify that. The whole topic of noise equivalency or depth of field equivalency is completely separate and I just mentioned it to make it clear what part of a camera influences which characteristic (light density for exposure, pixel density/pixel size for noise, sensor size for depth of field)
That difference is exactly what I'm talking about. You'll generally find that a cell phone photo has about the same noise once if you divide the ISO by the square of the relative crop factor (and set exposure accordingly). Coincidentally, you also need to use an aperture that's faster by the relative crop factor to get the same level of background blur.