This isn't strictly true -- an automation could come alongside a (substantial) productivity improvement, growing the firm to the point that it's total headcount still rises.
If there's consumer demand for more (and cheaper) versions of whatever product, then rather than a single company this form of automation can grow the industry as a whole too.
Inevitably, however, there will be industries that don't really need to grow. We'll just get what they make cheaper without buying much more of it. But then we'll have extra money (and extra people willing to work) -- figuring out new things for those people to do, possibly in wholly unrelated industries, is the very essence of why most of us still have jobs despite centuries of automation.
Aside from the productivity argument, a big problem businesses face is finding capable and reliable people. If you can push that problem onto the companies building robots, it might not save you any money, but it reduces your own risk and that is still going to be worthwhile in many cases.
If there's consumer demand for more (and cheaper) versions of whatever product, then rather than a single company this form of automation can grow the industry as a whole too.
Inevitably, however, there will be industries that don't really need to grow. We'll just get what they make cheaper without buying much more of it. But then we'll have extra money (and extra people willing to work) -- figuring out new things for those people to do, possibly in wholly unrelated industries, is the very essence of why most of us still have jobs despite centuries of automation.