Just curious, did you try having faster base movement for the main character before implementing the dodge? Many arcade shmups give you the option of having ships of different speeds and shots or in the case of some PC Engine shmups, giving you the option to switch between ship speeds. You'd be surprised how many shmup superplayers can control a fast ship even without a focus shot mechanic.
The game briefly had speed power ups but it didn't really add anything to the game, other than an extra pick up. The dash came in after that as I felt it was a more interesting mechanic. Faster movement is just a stat increase, but the dash can be used for temporary faster movement or to dash through bullets, it also has risk/reward if you fail and is tied to the scoring mechanics by generating score if you dash through bullets.
Another reason is the game is not exactly the same as traditional shmups due to no vertical movement. Likewise a dash mechanic would be harder to integrate in a traditional shmup I imagine.