I agree with this in 99% of cases (gotta leave a bit of room for the late-blooming geniuses). But you forgot something...most writers aren't 'really good' at dialogue because most writers aren't 'really good' at every aspect of writing.
If the goal is to go from 'really bad' to 'good enough'? That's attainable for someone who realizes that robots are doing the yapping. The OP isn't a hopeless case...just needs to back up a bit.
Here's an alternative to reading your own work aloud (which to me sounds like a good way to solidify bad habits, but it seems to work for others).
In addition to keeping to your reading/writing schedule, pick 4-5 contemporary writers whose dialogue you admire. Make sure that 2 of them are amazingly good, that 2 of them are merely passable. Read their dialogue over and over and over and over...write it out. Write it again. And again. Read it aloud if you must, but I'm not sure it's necessary. Did I mention doing it over and over? Then scoot over to the SYW part of the forum and eavesdrop for a while. Then start all over again. Add in some fresh writers this time. When you start mentally editing the passable dialogue, you know you're where you need to be.
It's a lot of concentrated, dedicated work, but I think it also happens to be the fastest, surest way to improve.
) It sounds like just the kind of homework I need to be doing, along with getting to know the one character better.