Why are top-mount joist and purlin hangers shorter than actual lumber dimensions?
Besides safety and practicality mentioned by isherwood... part of the answer is money... the size of the hanger is related to the cost of the hanger. If you make or sell hangers in bulk, then every cent matters (customers like walmart and lowes will buy the hangers that are one cent cheaper per 100 boxes). If you only need to hold a certain weight, then there's little benefit to oversizing the hanger. 

Another other part of the answer is that purlins are part of a (steel) roofing system. You cannot have the hanger sticking through the roof.

But If we are just talking about joist hangers in general, tops of the joists will be level with the header if you install them level. The hangers that wrap around the joist will need room below the joist (just the thickness of the hanger - not very much). 

Where joists are the same size as the header, hangers that wrap under will be protruding at the bottom (if the top is level). Sometimes that doesn't matter, or if it does, then using hangers that don't wrap around the joist are necessary.



EDIT- After seeing the second edit to the question, I now understand the issue. I think you could notch the joist (1/8") to fit in the hanger (or use a different hanger).