Capn Bloggs:
The Vertical Error Budget was developed so the designers could use less obstacle clearance in the final clearance of an RNP final approach segment than that used in LNAV/VNAV approaches for the unbathed masses.
The OEM has to perform additional tests that demonstrates a particular airframe type's Baro VNAV system performs better than the standard Baro VNAV system.
The "budget" comes in when the designer calculates the RNP AR final approach segment required obstacle clearance, which is proportionally less as the RNP value used decreases from RNP 0.30 to as low as RNP 0.10.
I'm not an engineer nor a designer but it seems to me some of it is based on smoke and mirrors.