That’s not a common phrase, though…
Those are very small percentages. Maybe it is a phrase some people use, I’ll accept that, but it is not common.
Compare with an actually common expression
Most phrases have very small percentages, as they are measured against all other combinations of words in literature.
Since it’s an informal idiom, it’s also much more common in spoken than in written language.
Even with those small percentages, ‘free as a bird’ was twice as common.
Again, “happy as a clam” is very informal. “Free as a bird” is much less so, so it makes sense it pops up more often in literature.
Also more poetic, shows up in poetry and song lyrics, pre-written spreches, etc.
You are literally showing it’s half as common as “free as a bird”, a VERY common phrase.
That only proves it’s common!