Certainly could have been worse. Good for everyone involved that no one was injured.
In my opinion, now would certainly be the best time to introduce the customer to the electronic starter idea. For a number of reasons we typically site for switching mechanical starters out for an S.S. unit, sealed in contactors as such in your story is not one of the things I typically reference. However, I think it covers to the extreme what could " possibly happen" with the old mechanical type starters. I'd bet your customer seriously considers the idea.
Over temp contacts on the motor typically catch this to shut the run contactor off, but as it has been said,with a sealed in contactor, ain't nothing gonna stop it short of 3phase power removal.
I'd be curious why (not that it would have mattered) the smokes didn't trip? And the shunt trip device in the machine room? Maybe it didn't get hot enough? Or...nothing works in the equipment room regarding fire code. Now's the time to push that issue too.