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I have worked in a CVS so I can answer this first hand. The main reason is every CVS is critically understaffed to the point of danger to patients.

Beyond that systemic problem that adds delay, actually dispensing the prescription is not the rate limiting step. When you get a prescription there's a whole list of things you need to do before it can be dispensed. In no particular order:

1. Select the right drug which seems easy but the prescriber may have used an old brand name, or misspelled it, or put in something that doesn't exist.
2. Calculate days supply (easy for pills, not so much for insulin, creams, eye drops, etc.)
3. Find the correct doctor in the system
4. Find the right patient's profile and see if they really fill at your store
5. Transcribe the directions in a way that makes sense in less than ~200 characters to fit on the bottle.
6. Check to see if the patient already has another prescription on file they are in the middle of the refills for so you don't have two active prescriptions.
7. Check to see the prescription has all the required information on it to be filled based on state requirements
8. Send the finalized prescription to the patient's insurance which inevitably is rejected because of some minor issue with any of the above, or it is expired, or requires prior authorization, or they changed their name, or it is too soon, or it's not the proper moon phase.
9. Actually fill the prescription which requires finding it on the shelf which is a mess because you fill ~500 prescriptions a day
10. Scan the bottle to make sure it's the same as what you billed the insurance, but if you picked the wrong generic brand on the first step you get to start over.
11. Clean the counting tray
12. Count the pills
13. Get the right vial and label everything with the stickers, and if you need more you need to print more out but someone else has a 50 page print job ahead of you and it's out of labels
14. Answer the phone
15. Answer the drive through
16. Answer the patient at consultation
17. Answer the patient at the cash register
18. Send it to the pharmacist for review which is a huge process on it's own which requires looking for interactions, appropriate dosage, correct drug for the disease indication, and simply reviewing you got everything transcribed correctly which if it isn't you get to start all over. Plus there are 50-100 prescriptions already waiting for review.
19. Process a vaccination patient
20. Add water to a reconstitutable (powder) medication
21. If Poseidon wills it, the prescription is approved and then you get to bag it, then put it in the right spot in the bins so it can be found.

If it's a controlled substance you need the pharmacist to do about 50% of the steps above and access the safe which is a whole process. In the meantime they are on the phone with a doctor or some insurance trying to get something clarified or approved. Or compounding someone's diaper cream. Or doing vaccinations. Or counseling someone on their antibiotic. Some drugs have mandatory monitoring programs you have to enter information from the doctor before they can be dispensed. Some drugs require a dosage syringe, or intramuscular syringes, or needle tips.

Suffice it to to say it is an involved process.