Hmm, do you realize, that even if you have 1B probes everywhere. You're still bound by speed of light communication speed, right?
It's faster than probe speed in this age, yeah. But still not enough, if we're talking distances to other specific planets, stars, etc.
Two possible ways to solve this, humans will become immortal or speed of light bypass method will be discovered.
the post office has utility even if the messages have very high latency.
also if this probe network reduces the transmission costs to normal terrestrial levels (and not requiring , say, a 400kw tx dish..) it could drastically increases the utility of the link -- and all of this without discussing how much bandwidth a link network across the stars might possess compared to our current link to Voyager..
(this is all said with the presumption of a reason to have such distance communications channels.. )
Seems like the problem OP is trying to solve for here is not latency, it's signal power and redundancy.
You're exactly right and thank you for carefully reading! I very explicitly said that there was a multi year round trip for information even in the best case (e.g. Alpha Centauri), to get out ahead of the well-actually's.
As you noted, some of the gains could be signal power, redundancy, the ability to maintain a quality signal over arbitrary distance; but most importantly, seeing the universe from the perspective of the lead probe in the relay, some arbitrary distance away.