Look up Bob Conley who ran as a D from SC vs Lindsay Graham. IIRC, he ran well to the right of LG, who basically said that Conley was too conservative.
Look up a calendar.
Again, what would it benefit?
A candidate like that would have no reason to run as a dem unless they had other Dem beliefs - like being pro-abortion. Which you say you don’t mean.
Explain how this would be good?