You can not really blame a clinic for not having the capacity to take an additional case.
Yes, living in the NoVA/DC area we are lucky with numerous options.
Edmonton/Alberta/Canada - our local ER vet has had a few occasions where they have just stopped taking new intakes for an evening (not even a waiting time, just a “don’t bother coming here”). Fortunately there is a second seven day a week ER, and a new Friday-Sunday ER has just opened. The vet shortage is very real and needs to be addressed. Also significant burn out of techs and receptionists from the addition work during Covid + the abuse they faced by clients who didn’t accept not being allowed in the clinic for appointments.