I've been told/read that native speakers rarely use 'nous'; preferring 'on' instead. If that's the case, is 'tait-on' an accepted (generally; not by Duo) replacement, or is it grammatically awkward for reasons I don't (yet) understand?
There is no 3rd person form in the Imperative, so using "on" is not a possibility.
Incidentally, if it did exist, it would be "Tait-soi !", because "on" is a Subject Pronoun, not a Disjunctive Pronoun.
Does this need the 'nous' Other instances of 'let's do something' carry just the verb, ie 'Taisons'
Yes, it does - because it's a reflexive verb. As a statement eg we are being quiet, it would be nous nous taisons. So as an imperative, it needs the reflexive nous ie taisons-nous.
Does the absence of the hyphen make it wrong?