no earthly use, reason, etc.

no earthly (something)

No conceivable or practical (something). You had all day, so there's no earthly reason you couldn't have finished this on time! It's very sweet that you bought me a laptop, dear, but I'm 85—I have no earthly use for one of those things!
See also: earthly, no
Farlex Dictionary of Idioms.

no earthly ˈuse, ˈreason, etc.

(informal) used to emphasize that there is no use, reason, etc. at all: There’s no earthly reason why she shouldn’t come with us.
See also: earthly, no
Farlex Partner Idioms Dictionary
See also:
  • no earthly (something)
  • no earthly reason
  • no earthly use
  • (as) good as finished
  • finished
  • let (one's) heart rule (one's) head
  • let your heart rule your head
  • not stand an earthly
  • not by any stretch of the imagination
  • by no stretch of the imagination