I wonder what experts would actually want out of a sideline tablet system.
The primary use of the tablets is to consume and analyze new information generated during the game.
But, practically, due to NFL rules, the only thing that the tablets are allowed to do is display still photos of past plays. [0] They've replaced B+W printouts of photos in this role.
Coaches can get the photos faster on the tablets than with the printouts, which can be a huge advantage. But if the system is unreliable, then they might get them slower, or not at all, and waste valuable cognitive capacity on the fucking goddamn malfunctioning tech that is keeping critical information from them in massively time-sensitive situations.
That I think is what's happening with Belichick here. He's notorious for preferring reliability over almost all other considerations. Though I imagine that if full replay video were allowed, it might have gone further before hitting his "fuck this" point.
Also note that there are also team staff (often the offensive/defensive coordinators -- the 2nd level of command, immediately after the head coach) in booths up above the field, with (I think) no technological restrictions, in radio communication with the sideline staff.
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[0] http://www.sbnation.com/nfl/2016/5/24/11715128/nfl-competiti...
For an illustration of what all this "analyzing past plays" stuff actually means in the context of football:
