2) Will the #14 wire be adequately protected by a 20 amp CB, according to the NEC? Absolutely not.
It's all about protecting the wiring, not matching the wire as closely as possible to a small load. That's why we can't wire lighting circuits with 18 gauge wire.
That's what I thought the code wants. That if one problem happens (overcurrent due to a fault) you don't cascade to a bigger problem (house fire). Because the breaker kicks out.