Most business do not require on call for their internal tools
Depending on the area of logistics OP is in, it's not unlikely that he'd need on-call engineers for his logistics management system. Blockages in supply chain can be extremely expensive.
At my company, downtime is approximately $50k/hr in a 24/7 environment for manufacturing and logistics. We're ALL on call.
It was brutal, but the mentality was - it's brutal now but you have the power to fix it, so engineering hours went into fixing broken windows.
That adopted mentality pays off tech debt fast.
Sure; but eventually you've got a bus number problem and a "I want to be able to take a vacation and I want my coworkers to be able to take a vacation" problem, and that requires more people.