The principle says important functions belong at the endpoints, because only they know enough; network help is a speed bonus, not a guarantee. NATs and firewalls are middleboxes that put important jobs in the middle.
They exist for real reasons (IPv4 shortage, cheap perimeter defence) but they do not refute the principle: true guarantees (encryption, authentication, access control) still live at the endpoints.
The trade-off is "remembering things" vs "just forwarding". The internet scales because core routers are simple and forgetful. DPI looks deep into every packet and matches attack signatures, needing memory per conversation and heavy processing, so cost grows with traffic x conversations x signatures - exactly what does not scale. It is also blind to end-to-end encryption (TLS/QUIC). Resolution: keep the core simple/stateless; do security at the endpoints; inspect only at the edge or on samples.
Principle: important jobs at the endpoints. Middleboxes (NAT, firewall, DPI) violate the simple transparent network but persist as trade-offs. CDNs (anycast + edge caching) put content and some processing inside the network, but a CDN is really an application-layer overlay built by endpoints, exploiting routing and performance - which the principle allows. So CDNs stretch the principle rather than break it; real correctness jobs stay at the endpoints.