Once upon a time, there were no powered compound miter saws, and everyone worked with solid wood instead of ply. In those times, the radial arm saw was king. However, compared to today's compound miters and table saws, the radial arm saw has been superseded in most metrics. They present a bit of a safety risk in that most of them cut as you pull towards yourself, on the climb, which magnifies bad technique and can cause skipping with the blade coming towards you.
When they are adjusted well, you can use a radial arm saw to do some novel cuts, particularly with a dado head and a high tolerance for fear. However, a modern compound miter takes up a lot less space and stays square better. Compared to a table saw, the radial arm has less capacity to work big panels, and is a bit more challenging to do small, intricate work. There is nothing 'wrong' with it; technology and building materials have simply moved on.
For me, space in my shop/garage is at a premium, and I have a large table saw and two compound miters already. I've turned down several similar opportunities on old Radials over the years. If I had a lot of space, I'd take one in, but it's range and limitations are not worth it for me personally.