We deal with a number of carriers and find that some will call us after hours if there is an issue (meaning they have someone actively working on it from the office, from home, or from the truck, we have our 24 hour dispatch number on our load sheets that allows us to help carriers get our shipments together set up.
That being said, sometimes our freight will sit on a dock or in a trailer over a weekend because they couldn't be bothered to pick up the phone and call us. We're here to help, we're here to reach out to an exporter/importer if new paperwork is required or if a customs broker has some issue with the clearance.
Bottom line: the sensitive freight, that which 'needs' to get there, freight where we NEED to be contacted with any delays go to carriers that have the ability to service us and our clients properly. Note - those shipments usually have a higher price tag, so really you pay for what you get!
Keep well,
Mike