Do You Think Healthcare Companies Should Design Patient Experiences Like Customer Experiences?

No. That would be an utterly despicable act.

Patients are patients, not customers: they are people in distress who need medical attention.  They have a reduced capacity to look after themselves.  Any attempt to consider a patient as a customer is an abuse of power.

The customer is a customer when they buy their healthcare insurance, and in that circumstance it is reasonable to treat them as a particular kind of customer.  But when they become a patient the healthcare provider has a duty of care towards them, which means that a customer-vendor relationship is not possible.  Treating as patient as a customer is abuse: prison sentences might be appropriate for the management in some cases.

An analogy might be a lost child wandering into a factory or shop.  Is it ok to treat them as a customer? No.   You would look after them, not employ sales tactics.