The world would not actually be improved by having 1000s of customer service reps genuinely authentically feel sorry. You're literally demanding real people to experience real negative emotions over some IT problem you have.
But it would be improved by having them be honest and not say they’re sorry when they’re not.
People authentically, genuinely, naturally care about other people; empathy - founded at least partly in mirror neurons - is the most fundamental human nature. It's part of being social animals that live, survive, and thrive only in groups. It's even important for conflict - you need to anticipate the other person's moves, which requires instintively understanding their emotions.
The exceptions are generally when people are scared, and sadly some people are scared all the time.
They don't have to be but they at least can try to help. When dealing with automated response units the outcome is the same: much talk, no solution. With a rep you can at lease see what's available within their means and if you are nice to them they might actually be able to help you or at least make you feel less bad about it.