Contact Centres aren't cheap, but Third Party ones are very much cheaper, they can also "flex" demand better. Phone is the most expensive contact form though, so everything that can be done to push customers to other contact methods is always done. Customers may not appreciate it, but going to the website does save lots of money for the company, thus making the customers product ultimately cheaper. Having 24/7 contact centres comes at a price. Companies have to tread the line between having contact available at all times, and the cost of providing it.
Companies can (and do) see how many calls are coming in when they are shut, so can work out if it cost effective to open. At my (non-railway) Contact Centre we close the phone lines an hour earlier, and at the weekend, and only have webchat and emails as contact at these times, to make it cheaper to run, but still provide a service. We are also totally in-house and not outsourced