We shouldn't have a unique address but rather give a unique random token to anyone asking for our email address which could be severed (or bound to receive from a single address, ie that counterparty can not transmit that token to anyone as my server wouldn't receive mail from another address).
We should have systematic guarantees that the sender is the mailbox it pretends it is.
Encryption in smtp should be mandatory.
We should have an easy to use content encryption (pgp style).
Ideally you would like to decorrelate the address from the service provider (lots of people are prisoners of gmail, hotmail or their ISP).
I am sure we can make the chistmas list much longer but to me these are the major issues with the current system.
Address exhaustion is a real issue though, so you will need to acquire many email-worthy domains for this service.
As you mention we can use aliases for unique emails (which is what I do, but I had to create a software on the side of my mail server to manage them, as my mail server never intended to use aliases that way, and for instance makes the list of aliases visible to everyone on the server, and does not allow to assign a keyword to an alias).
It is possible to have guarantees on senders by using spf and dkim, but not many server actually use them and you currently can't make it a hard requirement for your incoming traffic, so pretty much useless.
Smtp encryption has taken a step back with TLS, as with STARTTLS we are now forced to use optional encryption that can be downgraded by a MITM, whereas before one could elect to only have an SSL port open.
Content encryption is possible using PGP but clunky and almost no one uses it.
And people can buy their own domains if they know it is possible and how to configure a DNS server, needless to say not many people do.
What I suggest is that we would need a protocol that does all that by default.