This isn't the case in NY from my understanding as I've seen psychiatrists send ADHD prescriptions digitally to both physical pharmacies and delivery pharmacies (Capsule). So it might be a restriction imposed by your state.
This makes sense because information about controlled substance prescriptions are stored in a central registry so law enforcement or other government agents can review them easily. The federal regs only apply to controlled substances, so the e-script systems 'probably' direct controlled substance scrips to the DEA registry. But, the health providers, insurance companies, health systems, pharmacies networks/chains, and so on, are probably keeping a copy of everything.