In my 37 years associated with the broadcasting industry, I've run across the same situation. In fact, when I listen to some of my old tapes when I first started back in 1969, I can't imagine I sounded like that. There's no substitute for experience and it seems harder to get it these days with big corporations owning clusters. There's less and less opportunity for a newcomer to 'get their feet wet' in the business.
In your case, my advice would be to find something positive about that person's abilities. They may not be good now, but is there a chance they just need someone to point them in the right direction by giving them some advice on what they may be more suited?
I've heard popular market on-air personalities that really didn't sound all that great, but they're legends in their markets. And, they may be great as talk show hosts or DJ's, but you wouldn't want them cutting spots.
It could be that the person you're describing isn't right for certain on-air work. But they may be perfect as a show producer, audio editing work, board opping games, etc.
Also, there are times when a person is right for what they know about a subject. We were All Sports for a while and I found that the professional sounding on-air personality wasn't necessarily what we needed. I was looking for someone who could intelligently talk state and local sports. That may not always associate with a professional sounding voice. Fortunately, we did have a local weekend TV sports anchor hosting our morning show and his 'sidekick' added the local flavor. But, sometimes, the audience can relate more with the non-pro because he or she sounds more like them. It depends on the situation. At the time, I preferred having listeners know the person they're listening to knew what the hell they were talking about, than how professional they sounded.
Your advice to listen to other stations and announcers is probably a good idea. I think we all have taken advantage of that learning experience.
If you're not in a position that requires you to make the decision as to whether or not they get on-air time, then just let 'nature' take it's course. If management feels this person isn't on-air material, they won't use them. It's their decision. I was fortunate enough to start out on a small station where management allowed me to learn the ropes and make mistakes. There are a lot of people I have to thank for giving me the opportunities I've had over the years.
There are those who just have the knack for broadcasting. A friend of mine does a lot of voice-over work. He has one of those 'ballsy' voices that I wish I had. Sometimes you have to work with what you've got. Maybe your friend doesn't have what it takes.
Above all, be honest! The truth is like surgery...it hurts, but it cures.