You have to be building a lot of big flat things to justify the floor space a drum sander takes up. If you already have one, sure, use it, but floor space is by far the most expensive thing in most shops.
The power and dust collection requirements tend to be getting towards the bigger side of things for a drum sander as well. Most truly useful sizes are at least 240V if not three-phase.
I think that's an exaggeration, especially for cutting boards. Unlike thickness planers, most drum sanders have an open frame. Even the smallest 16" units can handle projects that are 30" wide. And these units work perfectly fine off 115V.
You can crank out cutting boards like that with not much more than a bunch of clamps, a small drum sander, a miter saw, and a good vacuum cleaner - garage-friendly and under $2,000. The issue is the hours of manual labor you have to put into this, especially since people are not used to paying hundreds of dollars for a decorative cutting board.
There are custom cutting board businesses out there, but they just use a CNC mill to cut personalized shapes or messages in common stock. That's a larger capital investment but far less manual work.
It's a huge exaggeration. My Supermax 19-38 has helped me produce cutting boards larger than any normal person would want and it's a 120v machine. It does require dust collection but so does a table saw, planer and jointer, which are other machines you'll need to make a decent cutting board.
Now drum sanders do take up space (though mine is on wheels and can roll to the side when not in use), and aren't the easiest machines to use and maintain. But when it comes to cutting boards it vastly reduces the labor. Most of the time is just waiting for the glue to dry.
The power and dust collection requirements tend to be getting towards the bigger side of things for a drum sander as well. Most truly useful sizes are at least 240V if not three-phase.