A stadium screen showing a replay is competing with the crowd's own memory of what just happened. That constraint makes in-venue video a harder timing problem than broadcast.
The audience already knows the outcome
Spectators watched the incident directly, so a replay arriving late has to hold attention for something already seen and resolved. Broadcast audiences have no such reference and will accept a replay whenever it comes.
A delay of a few seconds is tolerable, while a delay long enough for play to restart makes the replay an intrusion.
The useful window is short, and it closes on its own regardless of production quality.
Production takes time that cannot be compressed
Producing a replay requires selecting an angle, marking the clip and cueing it, and each step is performed by a person watching the same match. Automation can shorten the mechanical parts but not the judgement about which angle is worth showing.
Isolated camera feeds must be recorded and made available before any of that can begin, which adds a further short delay.
Venue operations run a smaller team than a broadcast, so the same task is completed with fewer people under the same time pressure.
Phones create a second reference point
Spectators streaming coverage on handsets see a picture delayed by many seconds relative to the pitch. The screen, the phone and the live action disagree, so three versions of the same moment are present in the same building.
That disagreement is most visible when a stadium reacts to something the phone audience has not reached yet.
Venue connectivity investment has made this more common rather than less, since more people now watch a delayed stream inside the ground.
Review decisions changed what screens must show
Competitions increasingly display review footage and decision graphics in the venue so the crowd understands what is being examined. A stadium left uninformed during a long check turns hostile quickly.
Those displays must be synchronised with the official process rather than with the production, which introduces a separate timing dependency.
Showing the wrong angle or an outdated graphic during a review creates confusion that is worse than showing nothing.
Screen technology outran the pipeline
Display hardware now supports very high resolution and brightness across surfaces far larger than a scoreboard. Ribbon boards, wraparound displays and full-roof surfaces are all now routine.
Feeding those surfaces requires processing that itself introduces delay, so a better screen can arrive later than a worse one.
The engineering effort in modern venue video sits mainly in shortening that chain, because picture quality stopped being the limiting factor some time ago.