Finishing, then assembling

Hey all,
Most of the major sub-assemblies for my second piece of furniture, (it's my first big project; the first piecce was an end table) are nearing completion. Finishing the thing all put together is going to be a pain, so I figured I would mask off the joinery, finish the assemblies (front and back face frames, left, right, and center panels, and bottom panel), and then glue up. Center panel fits into a dado in the bottom panel; bottom panel fits into grooves in the front and rear face frames; face frames fit into grooves in the left and right panels
Then I had an idea. Could I save time by finishing up the assemblies as they are now, only masking the edges that fit into grooves, and after they're all finished, then cut the grooves/dados? Cutting the grooves exposes new wood to accept the glue.
What am I missing?
Chris
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The trip across your tools (or your tools trip across the finished pieces). Believe me, your table saw top or your router base are not nearly as smooth as you think.
OTOH, I have found that finishing before assembly by masking off the glue areas yields a piece with a superior finish because you avoid all those impossible to reach corners and edges. It just takes a great deal more care, first in making sure you don't get finish in the glue areas and that you don't mar the finish during assembly.

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