Personally, I try to eat as wide a variety of foods as possible (that includes cheesecake!) I don't find just limiting myself to meat, or just to vegetables, or indeed just to cheesecake to be appealing.
I do it to cure (99%) a chronic condition (and it remains to be seen whether my gut will heal enough to allow old foods back). If I had a choice, I'd be eating a meat-based diet with rice and ice cream!