I like to make both, 'general purpose' rigs and 'one-offs', in production. Which type to use and when depends on how the rigs will be used throughout the production.
General purpose rigs are good when the character appears frequently and needs to perform most of the poses and action that appear in the storyboards. This easier to do when you know exactly what's expected as far as poses, camera angles and actions go.
If the storyboards haven't been drawn yet, building a general purpose rig becomes a bit tougher because now you need to anticipate what the character
might be expected to do and how the animator
might use the character, and you risk over-engineering the rig for animation it may never actually do. This excercise can get time-consuming and wasteful. In this situation it's best to get everything the character will do worked out between director, storyboard artist(s), and rigger/animator(s) before you start working on the rig.
One-offs are basically rigs that will only be used for a single scene or limited number of similar scenes. These are quicker to build because they only need to do a few specific actions as boarded. The tradeoff is that a lot more custom drawing needs to be created for the show.
In my experience with TV shows and personal shorts, I find it's efficient to create and use both types. I like to keep the general purpose rig's capabilities limited to the most common and typical animations, and make 'one-offs' for very specific actions or camera angles that would be too complicated to build into a general rig.
I think if the general purpose rig can perform maybe 60% - 70% of the animation, it's a pretty good rig. For scenes where the rig won't do, I'll set up quickly built one-offs, or maybe even 'multi-purpose' one-offs that can be repurposed and easily customized for other scenes as needed.
These days, I try to avoid building in too much complexity in a general purpose rig. When the rig gets too complicated, it becomes difficult to modify it to hit unexpected poses and animation. For an on-going series, the unexpected will ALWAYS come up. Try to design your rigs with that flexibility in mind and the animators will be much happier to use it.
My very first 'Anime Studio/Moho' project was a personal short called
'Scareplane'. The rigs in that cartoon were fairly primitive but worked well. Basically I built a general pose rig for each character that was capable of performing 70% of the scenes with slight modifications, and the rest were custom 'one-offs'. Many of these 'one-offs' were re-purposed for multiple scenes, sometimes with minimal modifications. This approach worked out well for me and prepared me for more complicated stuff that came along later.
I've learned a lot about rigging and animation in Moho since we made
'Scareplane' five years ago, and the rigs I make for TV productions today are a lot more complicated, but I still keep these rigging theories in mind.
Hope this helps.