It is becoming more of a theme at some clubs that a change of manager results in wholesale changes in coaching staff but an awful lot of clubs have staff set-ups they don't necessarily disrupt when managers/head coaches change. It's more likely a change in this area would need to be a feature request as to replicate it correctly it would probably need a couple of things like recognising which clubs would not partake in this, or which staff they would not let leave. For example, at Stoke, for a number of years Andy Quy was the goalkeeping coach that had to be accepted by incoming managers. He got on very well with Tony Pulis, but when Tony Pulis left he did not.
The fact they accept mutual termination is offered more as a game play convenience.