You are sorely mistaken. There are a LOT of laws and regulations regarding service and delivery of court documents etc, and using email will not suffice for the vast majority of them. How are you going to prove that someone actually received mail and it wasn't read and deleted by someone else with access to the account? How are you going to prevent sensitive documents from being read since email is wide open? Yes, I know, encryption, but that infrastructure is not available yet.
I'm quite familiar with the uses of mail regarding legal documents, which is why I said "correspondence." While service of process may sometimes be performed by mail, if the receiver is hostile they can simply not accept the service, which is why process servers are often used. And frankly, if we're reducing the USPS to only transporting documents requiring signatures they won't be able to stay in business anyway, and you'd just use FedEx. Nearly all documents filed with the court must be done in person, or as is becoming more common, by electronic submission. Nearly all subsequent documents in the matter can be exchanged between the parties as emails, attachments to emails and/or faxes (I haven't sent a fax in a long while).
As to your questions about proof of receipt of email, the same questions exist with regard to snail mail. If someone throws out a document you mail them can't they just say they didn't get it? Can't anyone open an envelope containing sensitive documents? Can't someone intercept the mail and throw it out? An email would be much easier to track through a server which could reveal when it was received, opened and/or deleted. An infrastructure upgrade for encryption isn't necessary most of the time. A simple password on a pdf file attached to an email will deter 90something percent of snoopers.
I agree we can't get rid of mail completely yet, but it's on it's way out and is used quite rarely now compared to even 5 years ago.
No, you can't do that with all legal documents, especially the ones that require initials or signatures or dated. Don't forget about different protocols/precedents/rules/regulations/etc. regarding those legal documents.
<<---is working in compliance field and amount of the paperworks are staggering.
I didn't say 'all legal documents' did I?

Electronic signatures are becoming commonplace on legal docs, though there are some circumstances that require original signatures. Hell, I don't even sign my e-filed tax returns anymore; I just enter my pin-code and type my full name. As touchscreens and scanning start becoming ubiquitous, you'll start to see the law adapt. It's generally slow to do so as most older lawyers and judges are generally conservative and traditional about how to do things. As the younger lawyers start taking over electronic documents, signatures, transmissions and filing will become the standard.