I haven't carried a camera with AE for some time, but that's not because I don't think AE is bad, it's just that I like old, manually-operated cameras.
I don't think I get any fewer poorly exposed shots shooting by eye than I did when I used a camera with a meter. I am a little more careful when I judge the light, but I doubt that I can judge the light better than a modern light meter.
There are many types of built-in systems, some are TTL types that read the light which comes through the lens, and then there are those which actually read off the film itself. The latter tends to be the most accurate type. My hundred dollar Nikon FE has a far better meter than my much more expensive M6.
On the other hand, the old clunker Yashica Electros don't even read through the lens, the meter is mounted above the lens, yet these cameras are excellent at taking pictures in various light conditions, particularly low light.
And, not all meters read the same. I compared three different cameras the other day, all the same make and model, all set to the same ASA, film speed, and aperture, and yet all three built-in meters gave different readings. I don't even trust hand-held meters, I have two different Sekonic light meters, yet both read differently. To check the accuracy of meters and metered cameras, I simply go outside on a sunny day, and set the ASA to 400 (I always shoot Trix). If the meter reads 1/500th at f/11, then I know it's in the ballpark.
I'm developing film in my kitchen as I write, I'll get too see how well I guessed exposure this week as I was shooting with an F and an S3, while carrying no meter.