With an HMI you can do things that are not possible or difficult to achieve with just buttons and lamps.
Change setpoints.
See analog values.
See timer values.
Change timer setpoints.
Display alarms with detailed alarm description.
Display detailed sequence information.
And you can simplify the hardware by removing redundant buttons and lamps.
But most important, by changing from hardwired relay logic and hardwired user interface to what is essentially software, you can standardise on a control concept where you maintain and improve the software gradually over time, so that you get a much BETTER control system. And there are goodies. You can have remote diagnostics for example. And an alarm system that logs the alarms and other stuff so you can see what has been going on.
But it will cost more in the short run.