> Nitpick: this assumes that you're holding the f number constant. In practice smaller sensors tend to be used with smaller f numbers, which somewhat offsets the effect (especially if you are not someone who's given to shooting everything wide open on your DSLR).
Well most phone cameras seem to be around f/2, some slightly above, some a little below. The archetypal nifty fifty is f/1.8 or f/2 as well, and primes in that range are usually available for most applications and reasonable in price. Slightly slower primes at f/2.8 are often also available and cheaper. So dit-for-dat, you'd expect a full-frame camera to have at least 6 EVs lower noise than your average 1/3.something inch phone camera sensor (crop factor of ~10, area difference of ~100, ld(100) = 6...).
Your entrance pupil metric is really just a roundabout way to compensate for the crop factor of the sensor to get to the same FoV. The relevant property for exposure is the f-stop.
F-stop is the relevant property for exposure, but not for the total amount of light collected by the sensor, which is what determines the noise level (all else being equal). Exposure is light per unit area.
I do think that focusing on sensor size is unhelpful when thinking about noise levels. Big sensors do not magically collect more light simply in virtue of being bigger. They can only do so if you’re able to put a bigger hole in front of them (again, holding constant the angle of view). The use of very wide apertures is inherently more practical with smaller sensors.
As for using wide apertures with a DSLR, this is of course possible, but only in cases where a shallow depth of field is acceptable. On a cell phone camera f1.8 will almost always give sufficient depth of field. Realistically speaking most photos on a DSLR will be taken a few stops down from that.
It’s undoubtedly the case that DSLRs have an advantage over phones in terms of noise levels, but you have to consider the whole optical system to estimate the magnitude of the difference, not just the size of the sensor.
Well most phone cameras seem to be around f/2, some slightly above, some a little below. The archetypal nifty fifty is f/1.8 or f/2 as well, and primes in that range are usually available for most applications and reasonable in price. Slightly slower primes at f/2.8 are often also available and cheaper. So dit-for-dat, you'd expect a full-frame camera to have at least 6 EVs lower noise than your average 1/3.something inch phone camera sensor (crop factor of ~10, area difference of ~100, ld(100) = 6...).
Your entrance pupil metric is really just a roundabout way to compensate for the crop factor of the sensor to get to the same FoV. The relevant property for exposure is the f-stop.