The problem of exaggerated recessive negative genes is always a danger, as with most mammals (I think). Without diversity in the gene pool, they may all become susceptible to the same pathogen or negative survival behaviour.
Extra pair fertilization broadens the gene pool, providing better balance against group susceptibilities.
Crows should have a harder time because they have more structure to support. If they were only territorial for a small part of a year, then their activities the rest of the time would be simply seeking food and safety. However, they are engaged in a full time job with feeding siblings, seeking adjacent groups to join (or not) or establishing new territory. There's no time for just hanging out. So the options to be a breeder are varied, but very structured, making it more difficult to get established in a long term relationship with a mate and the crow community at large.