Those servers need to independently operated and resistant to global compromise.
We don't really have a good template for a system like this. We have centralized HA systems and decentralized high churn systems like Bittorrent and Tor.
I've been intrigued by the observation that forthcoming "proof of stake" blockchain systems have very similar requirements in terms of availability and capacity to anonymous messaging systems. I wonder if we can use the nodes in a PoS system to bootstrap an anonymity system like Vuvuzela.