I don’t think there’s anything wrong with an author/illustrator sometimes writing picture books that they DON’T illustrate, or sometimes writing novels or something else – but no, I haven’t seen many popular illustrators who both write and illustrate picture books and also write entirely prose novels. I’m sure there (probably) are some, but… all the ones I can think of who do both PB and MG, their MG novels are very much also illustrated.
For example: Peter Brown (THE WILD ROBOT series), Adam Rex (TRUE MEANING OF SMEKDAY), Brian Selznick (INVENTION OF HUGO CABRET, etc), Lynda Barry (wrote the YA novel CRUDDY) – and I rep Phoebe Wahl, who is currently writing a YA novel that was just announced – all of these are MG/YA by well-established author/illustrators… but all of them are highly illustrated.
I don’t think, though, that that’s because the publishers “prefer” it, or are MAKING them illustrate or something like that? I’m sure if one of these creators wrote a really great all-prose novel with zero illustration elements, a publisher would be delighted by that as well. It’s just that… well, they are gifted illustrators, they probably think very visually and bringing a visual element to these books for older readers that makes those books even MORE special. I don’t think any of these illustrators would have pitched a completely non-illustrated book – it just wouldn’t make sense for these books. With no illustrations all of these books would still be good – but with them, they are spectacular, the illustrations are intrinsically part of what makes the books special. So…
I mean again – it’s all about the book. If you have a great all-prose novel up your sleeve, that’s fine, and I don’t think anyone would MAKE YOU illustrate it. I just don’t really personally KNOW of any popular illustrators who also write long-form unillustrated fiction. Though they might well be out there!
ETA: I thought of one! Kevin Henkes has written MG novels (non-illustrated)!!!