I see no reason why for proximate analyses, samples should be analysed in different rooms or with different equipment, assuming that the exact same methods are used. Sometimes (slightly) different methods might be more appropriate. Cleaning of machines - if prescribed - and glassware between samples, should of course be done
In trace analysis work, different choices might have to be made.
Not only food and feed, if anything needs to analyse for proximate composition, it can be analyzed in the same laboratories with the same vessels but glassware should be clean and dry.