Vitalik is consistently one of the most interesting people to follow in the blockchain space. Even his (5+ year) old writing is quite interesting, if nothing else to see how Ethereum's research thinking has evolved over time.
A few questions re: why "Ethereum is not going further than quadratic [sharding]."
The first reason given: there's a minimum number of nodes required for shard for safety guarantees. So, a couple hundred shards, each with 1000 users seems like a limit. But I wonder: 10 years from now, if the blockchain (maybe pipe?) dreams succeed, then why do we expect 1000 * 500 = 5M nodes? This seems like it's quite small.
Especially if running a node on a phone ever becomes reasonable, or at least participating in the data availability process is possible here, then why would we not go further?
The second reason for non-super-quadratic sharding is data permanence. But here, couldn't we design different shards with different appetites for data permanence. Sure, NFTs currently are forever, but I can think of many applications where users do not give a damn about data permanence, and even some applications where users would prefer if data was just forgotten about.
In which case, what's stopping us from saying "these shards, we save. The other ones, who cares about." We would want users to opt into such guarantees, of course, but it seems reasonably possible.
Of course, let's get a good sharded blockchain before we optimize for more.
I'm excited to see how sharding research continues to involve and drives the cost per TX (economic and environmental) down. Consider me a cheerleader rooting for you all!