factorize() on a dense matrix tests several properties to find an efficient factorization. If factorize is called on Symmetric or Hermitian types, it does not try cholesky(), but only considers bunchkaufman():

From the source

```
function _factorize(A::HermOrSym{T}; check::Bool=true) where T
TT = typeof(sqrt(oneunit(T)))
if TT <: BlasFloat
return bunchkaufman(A; check=check)
else # fallback
return lu(A; check=check)
end
end
```

Is there any argument against adding (analogous to factorize on dense matrices):

```
cf = cholesky(A; check = false)
if cf.info == 0
return cf
else
return bunchkaufman(A; check=check)
end
```