...it seems like letting the camera set the exposure and then using EC when necessary is faster.
I agree, which is why most of my shooting is in AP mode using EC and/or spot metering as appropriate. Manual is fine if I'm taking my time over a shot like a landscape, or in conditions with unchanging light, but I don't see any point in using manual when another mode will get the same result faster and more reliably.
Embrace technology - don't buy the 'auto is for wimps' kind of attitude. One day, someone will come along and say even manual is for wimps and that bulb mode, using the lens cap for exposure, is the only way for a true professional.
You and I (and many other photographers on both sides) have very different ideas of what "reliable" means. And this is perfectly fine - that's why both types of modes exist.
The settings that the camera guesses on can change wildly, depending on where exactly you're metering. Your shots will not always be consistent. If you're using evaluative metering, changes in things like the background can have dramatic effect on your exposures. If you're using spot metering, changing where you're metering even slightly can also dramatically effect what the camera thinks is "right".
I guess my main point is that the camera does not have an intuitive sense of what I'm photographing. It can only guess, and allowing it to guess gives it the opportunity to guess wrong. Will I guess wrong too? Absolutely, but it trains me to keep an eye on the histogram and adjust. Exposure will never be something that you should "fire and forget" unless you're taking snapshots. (Again, this is my thinking, not what everyone should think.)
Your bulb mode comment is amusing, but entirely misses the point. The camera is
good at precisely exposing the sensor for a specific time with a specific aperture. Nobody disputes this. What is disputed is whether the camera can automatically expose every frame properly. Some people think it can, and they use Av/Tv. Some people don't trust it completely, and they use Manual. Nothing wrong with either.