I recently had my 50 year old home repainted. On the suggestion of the contractor he used two coats of high quality Sherwin Williams top coat and no primer. Now I am concerned that the job will be compromised and the longevity compromised.
It depends on the condition of your home and the type of paint on your home prior to repainting. I never apply an acrylic over an oil base without a primer, because I want zero problems. It would have been better if the painter primed, whole house or where necessary depending on the situation.
According to Sherwin Williams, Duration (their best house paint) is self priming. But, they still recommend a primer for exterior use. This is a contradiction on their part. It is possible your paint job will be fine and last a very long time.
Keep an eye on the paint job. If the paint job fails it will occur around the windows and doors or the trim first.
I believe it is always better to use primer as the first coat and paint as the second coat. Paint is made to be a top coat. Primer is made to be a bottom coat. You wouldn't use primer as your topcoat. Why use paint as your bottom coat? If your house was in bad shape before painting you could be in trouble, otherwise you should be fine.