I'm glad Wimmex asked this question. I've heard that a few of the DJs on various music channels prefer to do their shows live, such as Pat St. John on 60s on 6. I guess they have that option. St. John also hosts Classic Rewind on Sat. & Sun. nights, so obviously those shifts are voice tracked.
The smooth jazz channel Watercolors has a voice tracked DJ named Lily during the day, but goes without DJs evenings and night. It had two but the afternoon/evening DJ died last year. I sometimes listen to Love (Soft AC), The Bridge (Soft Classic Rock) and Spa (New Age Music) which have no DJs. Because they are designed to be soft, having no DJs is not a problem.
80s on 8 has the former MTV VJs Mark Goodman, Alan Hunter and Nina Blackwood. They voice track, but I enjoy their insights and don't mind knowing they are not live. The three are heard from 7 a.m. to 1 a.m. seven days a week, so voice tracking is needed. Goodman also does an afternoon talk show on Volume, discussing topics about music and taking phone calls. So he does that live.
There is one channel on Sirius XM that has live voices 24/7. Fox News Headlines, which acts as an all-news channel. It promises to be live at all times. The anchors work one hour on, one hour off, for four hours. So an anchor heard at 6am also does the 8, 10 and noon hours live. The next anchor is on at 7, 9, 11am and 1pm. Obviously, many of the spoken word channels doing politics, sports and a few other topics, are live during the day, so they can take phone calls. Then they get repeated at night and weekends.