Money isn't the issue, it's lack of direction.
The Abramsverse is just that: an alt version of Star Trek designed for the sole purpose of rebooting TOS with modern filmography.
As far as a series: CBS has 2 choices: something on the small or something on the epic.
Small would be essentially having the focus on a purpose built ship.
1. Medical Ship. It goes around stamping out medical emergencies, with just enough leeway that it can get some epic stories in there without having devote more than an episode or two to the more epic story.
2. Crime fighting ship. A Crime Scene Investigation ship. (Personally I'm rather tepid about the idea).
4. Engineering ship. Sounds promising. Dunno if they ever got any suggestions on that. The stars are the limit on engineering stories.
I'm sure people can find a few more examples of a single ship series which can have plenty of stories without having to step on the toes of prior series.
The OTHER option:
Do an epic series. TNG and DS9 were both epic series, having plenty of individual stories, and some more epic stories. DS9 took it the next level when they introduced the Dominion War, and made it more of a week to week series, rather than just self contained episodes which could be viewed in any order. (Excluding a few 2 part stories, TNG didn't really have a viewing order for the episodes, and neither did ToS).
I'm fairly certain any series that CBS does, it will lend more to the week to week style, since people enjoy that, plus it lends itself to having an audience that is more engaged and likely to watch the next episode to see what happens. Most prime time shows are like that nowadays, and have been for many years.