Clean up internal interface and streamline a few implementations

[nsiccha]

Opening to keep track of:

@mhauru

• [ ] says: "The two-argument version of show should, according to the docs,"
• [ ] says: "This looks like something that could plausibly be hit sometimes. Could it a throw error rather than an @assert?"
• [ ] says: "Just a bit simpler, should be equivalent."
• [ ] says "Does [NutpieVar (and relatives)] have to be mutable?"