Although there are specific agencies that do certify machines from a functional safety perspective, machine safety controls / relays etc. are not yet mandated here in the US like they are in other parts of the world. OSHA is more vague about this issue in that they mandate general safety / guarding and accept machine safety control systems as a way to get there, but they stop short of actually requiring them so long as operator safety is achieved.
That said, many companies, especially those with operations in other countries or who are headquartered overseas, will require safety certification, which will mean compliance using safety controllers / relays etc. But given that your machine has already been in operation without that we can assume this is not the case, so anything more would be basically voluntary. There are good arguments to be made for upgrading, but again, no mandate.
One of those arguments that I have indirectly experienced is one of liability. If a worker is injured using a machine and their lawyer finds out there WAS a safer way to do the controls, they may go after the owner for not taking accepted measures to protect workers using available machine safety systems. I friend did work retrofitting a machine that makes rebar reinforcing cages for concrete pillars and although he used safety light curtains and through-beam systems to keep workers away from the moving parts, the workers found a simple way of tricking the system and someone got skewered. Their lawyer wanted to know why they didn't do a safety assessment and get certification, the owner claimed ignorance, but lost. My friend, the EC that did the work, was not found responsible because he was contracted by the owner without stipulation of providing a certified system, but his lawyer still cost him over a year's worth of income.
