My intuition is that every operation we do (start TCP connections, generate keys, backoff after a failed login, ....) reveals a tiny fraction of a bit about that hidden state, web assembly calling random over and over again probably reveals much much more, over time it builds up.
(anyone want to guess if there's a quantum computer attack here, it kind of looks like the sort of problem where there might be)
So I think that with a sophisticated enough attacker entropy does degrade, the trick is to replace that entropy at a faster rate that the rate at which you guess the worst case attacker might be able to guess.
For most people it probably doesn't matter, you're exposing so little state over time you're likely effectively as safe as the parent poster claims, it kind of depends on whether, in this age when we know that nation state actors are watching every packet that passes thru their hands, watching every thing we're doing online, are you interesting enough for them to spend the time and effort? does the US/5Is think you're not a Trump supporter? are the Chinese interested in your trade secrets? whi knows what the Russians think
As I mentioned above using /dev/urandom doesn't have a mechanism you can use to signal this guess about how much entropy it needs over time to be safe, prior to 4.8 we used to have a mechanism that said "give it some more entropy every N seconds, 60 by default" but that's now broken
(provided here a python applet that periodically drains a little bit of /dev/random entropy if it has plenty available to stir the input pool that /dev/urandom uses for its entropy source)
That's a lot of words because the LRNG is overly complicated. But let's make it clearer: what you're saying about every TCP sequence number "revealing" part of the "hidden state" is exactly equivalent to the argument that every byte of AES-CTR ciphertext is revealing the hidden AES key. If that were the case, AES would be grievously broken.
If you don't believe that AES-CTR and the LRNG are roughly equivalent, try this thought experiment: retain the initialization functionality from the current LRNG --- building a pool of mixed and hashed unpredictable data from kernel events --- and scrap the rest of the LRNG, replacing it with... AES-CTR, using a hash of the entropy pool as its key. Reads from random/urandom (or kernel random reads, as with your sequence numbers) just tap bytes from the AES-CTR keystream. Is every TCP sequence number still revealing a little bit of the RNG state?
The Python script seems entirely silly to me; once the first read from /dev/random succeeds, you're guaranteed to have a fully initialized LRNG, and every subsequent read from urandom will be unpredictable and indistinguishable from random. Nothing is served by updating the LRNG after that point.
What you wrote is magical thinking.
However kernel entropy is real, adding more entropy to the entropy pool is always is always adding more entropy. If the pool had 1000 bits in it and you add 5 bits from the kernel and a fake 1000 bits from a bogus external source it still has 1005 bits of entropy (however /dev/random thinks it will be able to extract 2005 bits)
We actually encourage our customers who are particularly paranoid to lie to the kernel about the quality of the entropy our RNG generates - saying the entropy quality is lower than it really is causes more good quality data to be mixed into the kernel pool (of course the defaults don't do this)
The kernel pools are actually quite small (4k bits) so there's a real practical limit to how much you can play this sort of game