My understanding of a difference between French and English in this context. Gleaned from multiple sources, and hopefully close to the mark. ( I hope it will be ‘corrected’ if not ). 

This sentence uses the common expressions in English ‘ you should have (seen) .. ’, and in French ‘ tu aurais (vu). .’ 

In English, effectively ‘you should have been there to see … ‘ - in English we generally ‘ignore’ that this sentence could be taken or used to mean that you were supposed to have been there, but you weren’t.

In French effectively ‘ (if you had been there), you would have seen ..’ . - unlike the English sentence, the French expression carries no implication of obligation, but proposes only that ‘ if you had been, it is likely ..’.  ( the conditional because it is not a certainty that you would indeed have seen .. )

Because of the ‘lack of obligation’, devoir is not used here in French. 

English has a very mixed bag of uses for would, could and should.  It would be difficult to cover all the possibilities that could arise but perhaps an attempt should be made ! 

In this specific case, a note on the translation may be helpful.