It usually happens in practice ("Sarah knows someone in security"), but there's no reason "devops liason" can't be an explicit 2nd+ hat for someone on a team to wear.
Centralized teams are necessary for budgetary reasons: one person on every team asking for a devops product will never make a coherent case to management for why it's needed, but a team will.
But having been on both sides of the equation, the central-decentralized relationship usually breaks down because there's always a new face on the right side of that equation, and that requires reteaching / recoordinating all the basics. More consistency on the user side (a hat) helps significantly.
And ultimately, it's a trust problem: do I (central person) trust this person who's asking me for something? If they're new to me... probably not very much. If I've been working with them for awhile... probably a lot more.
Looking back at the last twenty years, oscillating between central sysops and everyone doing their own thing (is that "devops" ?), I feel that an optimum requires both: local skills to iterate fast, central skills to consolidate. Striking a budgetary balance is difficult, but at least ensure that some local skills remain - sell it to central ops as a way to get the trivial demands off their backs !