Well, I for one, take the schizophrenic approach. Patients can leave a message for a refill. They are told it will occur within 24-48 hours. Some pharmacies fax orders and some send electronically. I prefer the latter.
I personally review the faxes that come in each day on the computer. It's very straightforward to do the refills right then when the fax pops up. I always do the electronic ones first, because sometimes there are both. I go through my messages and knock those out as well.
I have 1 MA I trust to do refills. She knows the rules well. Allergy meds less than 6 months since visit, no issues. NO antibiotics. Asthma preventive OK less than 3-6 (depends on the patient, she knows them well) rescue meds more than 6 months, or bounce it by me. Others, she will generally check with me first.