"Bands that write their own material" didn't even start being a regular thing until the 1960s. You can always find fault in someone complaining about how whatever current pop star doesn't write their own songs when Frank Sinatra wrote even less of his own. Nowadays that just seems largely limited to manufactured Top 40 pop...I can't think of any rock bands that have teams of songwriters behind them.
As far as cover bands are concerned, I think you either need to be a precise visual and aural recreation (e.g. The Musical Box, a touring early Genesis tribute who are scarily accurate in every conceivable way) or an outlandish comedic novelty (e.g. Mac Sabbath, a theatrical So Cal Sabbath tribute who dress as McDonald's characters and rework the lyrics to be about fast food) in order to work. Otherwise, I just don't see the point.