Learning to meter without light meter has its usefulness.
Imagine a situation when you are in the shade part of a street, the buildings behind you project a shade on you and your side of the street.
You want to take a picture of the other side of the road, a fašade of a church in white marble kissed by the sun. The clouds play hide and seek with the sun, and you have to be fast if you want that light in your picture.
The user of "sunny 16" just select that exposure and he has a picture which is very probably quite right.
The user of a hand-held incident light meter must cross the road, measure the incident light, read that it is sunny 16, feel stupid for a moment, cross the road again, hope that in the meanwhile the light doesn't change. Crossing roads in Rome is not funny, motorists "don't take prisoners"
The user of a reflected light meter (whether in camera or hand-held) must measure the light on the other side of the road and then remember to compensate for the inevitable mistake that the reflected light meter will introduce when measuring a totally white object. The amount of compensation is always a bit puzzling as you have to "place" the white zone etc.
Which of the three methods is faster while guaranteeing an acceptable amount of precision? One can take a fast shot with sunny 16, seizing the moment and accepting the risk of a small exposure mistake, and then take the time for a measured and reasoned light reading for "fine tuning".
More in general the usefulness of the "sunny 16 rule" (or, let's say, choosing exposure by sight between LV 12 and 15) is that no light meter is accurate without a bit of reasoning, and as Benjiboy says "should be considered as a basis, in light of the photographers experience before making the exposure". That requires a bit of reasoning before making ANY exposure. The "sunny 16" can sometimes be just faster and more reliable.
In-camera meters are influenced by the background which changes continuously (dark or light, abundance of sky, relation sun-camera-photographer in backlit situations etc.) and can be definitely worse than using sunny 16.
Using an automatic camera will not solve the problem or can make it worse. Automatisms are only an emergency device.
As an example, while taking a subject which has a certain degree of back light during the central hours of the day, the "sunny 16" will suggest LV12 with a decently high degree of reliability while automatic exposure with a reflected light meter will be basically useless. Making a mental compensation to the automatic exposure is IMO less reliable than the sunny 16 rule.
"Matrix" metering introduces a random compensation based on what the camera thinks is the main subject. How is the camera supposed to know whether I want a silhouette of the "Petit Caporal" and have the background correctly exposed in this situation, or the statue correctly exposed and a burned background?
How can a camera think in my stead? Matrix metering is the worse of the worse as I cannot even "compensate" it as I don't know what the camera choose as important. With sunny 16 one just chooses EV15 with a guarantee of a correct outer exposure, a correct silhouette of the statue, not much reasoning and predictable results. And no walking forth and back for measuring what light there is outside.
Learning to meter without meter can be precious especially for "street shooting" when there is no time to even look at the camera setting. You know that your camera is set at 1/125@f/11 (100 ISO). You see a subject standing in shade (EV 12). You turn your aperture ring 2 clicks more open, focus and shoot, mentally counting the aperture clicks, without looking at the values on the camera and without checking the in-camera instrument (which requires "reasoning", analysis of the background etc). Especially with B&W, street shooting can be just "turn 2.5 apertures more open in shade" and "turn 2.5 apertures closer" for sun, leaving the shutter speed fixed and operating the aperture ring with extreme ease and speed.