I would get rid of the green wire. A "non-functioning" tach may provide an unintentional ground which will shut the engine off. I don't know that it would cause points to erode prematurely, however.
I once had a mysterious lousy ignition issue from a wayward tach wire.
Carl

1952 5-window - return to "as built" condition | 1950 3100 with a 235 and a T-5 transmission