@Array Platforms
Great topic, and conscious it's one of those 'no one size fits all'.

Fully onboard with your thoughts, except when to bypass the Lead stage.
 
Repeat Customers, yes, but only if they are buying the same product or service.
If not, I suggest it would be wise to still use a Lead qualification process, albeit slightly modified. i.e. use a dropdown to state if existing customer or new business.
 
Referrals are great, but not a guaranteed sale, hence suggest again to qualify using Lead process.
 
Therefore to us a Lead is a 'Sales Enquiry' rather than an unqualified prospect.
 
Over the years I've found that companies with low Opportunity conversion rates also have a weak Lead qualification process.
As an aside, this is sometimes driven by management pushing for a high Opportunity pipeline above all else.