you could have an empty chair and things would still get done
in general there are too many useless or noise making people in companies i worked in
when they go on holiday the work continues in peace
There is the strategy side of things which you won't get from talking to customers, but I've seen many cases where senior management make absolutely terrible (and obviously terrible, not only with hindsight) strategic messes, so I'm not totally convinced that senior management are necessary for this part either. Senior management do usually have a better overall picture - eg. that some product is losing money and some other product is growing rapidly - but that's usually because detailed revenue numbers are hidden from everyone below the C-suite.