I like that Silva has a lot more to lose reputationally by failing than either Koeman or Allardyce did; both could fail here and still be looked at for other decent football jobs. For Koeman, his success as Southampton and his personal reputation as a player were enough to make sure he's able to get manager jobs even if he didn't perform here. In Allardyce's sense, the jobs he's apt to take (relegation fodder) would be his this coming season whether or not you view his term here a success or not. No doubt Silva's got skin in the game with this appointment. He fails and his own reputation would take a massive hit.
The other sense is that you felt like both Koeman and Allardyce could be arsed whether or not they took the Everton job; Koeman didn't seem to want it initially and same with Allardyce. Silva wants this.