I don't get it. A carpenter's bevel is used when you don't care what the angle is. You just care that the angle matches.
If you want a bevel with a protractor built in, why not just buy a bevel protractor? The come in cheap versions for under $10, inexpensive digital stuff, down to high grade vernier and dial style that will easily get you splitting tenths of a degree.
This should suit your needs for about $8:
These are about 3x the price, but get you 10x more accuracy too (around $25):
These are suspiciously inexpensive at $20 (I don't blindly trust cheap digital gauges):
I use one of these (they're about $30) when I need fine angle measurements: