There are several good answers. One concern that's not currently mentioned in the other answers is when the initial guess is poor.
While most programs have several methods to perform an initial guess, and these are usually fairly good, they can also fail.
As a simple example, let's consider the superposition of atomic potentials:
J. Chem. Theory Comput. 2019, 15, 3, 1593–1604. It works well and it's conceptually easy to understand both why it should work and cases when it can fail.
If I want to converge this calculation of benzene, I'd start with the atom potentials from six carbon atoms and six hydrogen atoms:
Not surprisingly, this is a fairly good initial guess and the SCF can converge.
This one is harder to converge. I stretched all the bonds by $3\times$:
In this case, how do I treat the atoms? Are they individual non-interacting atoms? No, the bonds are stretched a lot, but there's still some shared electron density.
I can probably still converge this "stretched benzene," but it's harder because the initial guess is often tailored for covalently bonded carbon.
Problems with poor initial guess can happen more for unusual charge or spin states, or with metal centers. For the latter, consider that small differences in geometry could lead to different spin states, etc.
(Some programs I will not use for inorganic or organometallic calculations because the initial guess are routinely poor -- although most programs continue to improve.)