I actually see Beeminder as a form of behavioral therapy, in that it focuses on changing your behavior and provides incentives to do that.
I think Beeminder is incomplete, in that it doesn’t address the deeper inner conflicts that prevent you from doing what you want, but it was never supposed to be a complete solution, just a way of dealing with akrasia and correcting for hyperbolic time discounting (“five years from now, I want to have been sober for four years and eleven months,” as The Office put it).
It’s just a part of your complete breakfast!
For that matter, CBT doesn’t address the deeper conflicts either, and has often been criticized on those grounds.
The psychodynamic approach to therapy (examples include Internal Family Systems Therapy, Focusing, and Coherence Therapy) takes a deeper approach by having you look at and embody your objections, rather than just trying to counteract them by pushing them away and argue against them the way CBT does.
Beeminder, like any tool, can be abused. Making it shame-based is one obvious way to do that - clearly shame is counterproductive. Another way is setting goals mindlessly, so you push yourself hard to do something you really don’t want to do (like a degree or a career choice you don’t really want but feel pressured into).
A good solution is to beemind time to reflect on your goals. My new daily schedule includes a goal for vision thinking, where I take time to think and write about a vision for my future, as well as a goal for time to examine what my objections are and look at them closely.