Yes, people who can write often play at some level or at least know enough theory to be able to write stuff out, though we're not talking about classical and opera, mind you, where you really need some composition skills, but basic Pop/Rock/R&B/Country "songwriting". Some people just write the lyrics and hum the melody...and that's the start of a "song".
Thing is....I know people who can "play" the piano and the guitar enough to come up with songs...but could never play those instruments well enough to record.
Recent true story...
The female singe I was working with this summer was one of those people.
She sang in Rock bands for 20+ years and had a pretty good voice, and she said she had some formal training in piano....but she couldn't/wouldn't play any keys for recording, and her songs were basically lyrics and melody...she didn't even know what the chords were to her own songs. The "demos" she gave me...someone else came up with the chords and played the instruments for her.
The funny thing was....she thought that working with me, she was recording "her solo album"...

....meanwhile I was doing 95% of the recording work, and all she did was come in to sing a few times. I even had to take her lyrics/melody and figure out the chords (not a big deal) and then arrange all the music so that we (err, I mean, so that I) could than do all the tracking for the songs.
When she said that...about how she thought this was her "recording her solo album"....we kinda went our separate ways.

I mean, I wasn't going to spend countess hours doing all that.....on "her solo album".
Anyway...there are those people out there who need someone else to pretty much do everything. So, if they have the money to pay for someone else to do it for them...they pay for it.
Not any different than hiring session musicians/arrangers/singers.....something that's been going on since recording began.