Moral of the story: Fire bad clients.
* this client is giving me xxxx $
* it costs me yyyy $ for salary team... so there's so gains... so let's no lose the client (even if it means dumb work for the team)
Moreover: it's easier to justify the contract's cost (we have to monitor closely your infra to get your IT business running... here are the numbers of tickets that we processed) than having to explain: "OK, we did nothing this month BUT you pay us because MAYBE SOMEDAY something bad may happens"... because the client might either think that he doesn't need the support contract or that he doesn't need to pay that much...
All in all: it's not a bad thing for the team to leave that kind of bullshit job