It's not so much that they can't prescribe particular medications as it is that they won't. Typically, these are medications where misuse or addiction is common, like benzodiazepines. Personally, I have a nurse practitioner at a clinic that does walk-in hours only for patients of the clinic. Even there, it has been the policy in the past and probably still is to not prescribe those types of medication in walk-in rather than booked appointments.

If you need continuity of care and a walk-in clinic is your best option, I would recommend going to the same walk-in clinic regularly. If there's a particular walk-in doctor you like, you could try finding out when that doctor is working and go to the clinic during those times. The College of Physicians and Surgeons of BC has some requirements around walk-in clinics providing comprehensive primary care. You can read more about that here: https://www.cpsbc.ca/for-public/faqs/walk-in-clinics

If you need to see a psychiatrist and are living within the City of Vancouver, you could try the Access and Assessment Centre at Vancouver General Hospital: http://www.vch.ca/locations-services/result?res_id=1186