There is precedent for network providers clamping down on piracy even if strictly speaking they have no reason to care about copyright infringement. Many ISPs at the last-mile level attempt to block use of protocols like BitTorrent, because they charge a fixed cost to their users and this piracy guzzles much bandwidth they could instead allocate to more profitable customers who use little bandwidth each. The fact that much of the use of these protocols happens to infringe copyright is just a convenient pretext for the blocking. Although of course the situation is different for a higher-level provider like AT&T, similar incentives may exist.

There are purely engineering reasons for wanting to clamp down on peer-to-peer: a hierarchical Internet structure with a small number of servers piping content to many clients is probably easier to handle than a more evenly distributed one.

I also see a connection to network neutrality here, but not a purely legal/political one. Under a discriminatory pricing scheme that AT&T may be planning to implement in the future, communications from large companies' servers would likely pay more money to AT&T than peer-to-peer communications between consumers. AT&T may perceive that the X% of their bandwidth used for peer-to-peer piracy is wasteful and could be more profitably allocated elsewhere.

In other words, I don't think AT&T at all wants to analyze HTTP connections for pictures, as you suggest. That would indeed be horrendously inefficient. They are probably mainly interested in stopping bandwidth-guzzling movie piracy via peer-to-peer protocols such as BitTorrent.