He did not ever specify on or off chain or any specific restrictions in correlation to the use cases.

Then why he was against putting BitDNS on Bitcoin? See? If you want non-monetary use case, then use your own "dataset", to not disturb regular users, and take down their payments. Edit:

Why did Satoshi not create a block explorer from Day Number 1?

1. Because everyone had a full node, so no "block explorer" was needed. 2. For a working system, you are mainly interested in your own coins. If you have enough knowledge, then you can explore someone else's transactions, but a regular user doesn't need that feature. If you use traditional cash, you are interested in your banknotes, and not in reading serial numbers, and guessing, which of your neighbours had it in the past.

What conversation did they have to determine a block explorer was required?

https://bitcointalk.org/index.php?topic=1727.0

How many people were interested in block explorers?

Mainly those, who wanted to observe their peers. If someone was interested only in its own wallet, then that person didn't think about any kind of block explorer. However, when more and more people thought, that everything is anonymous, and works like Monero, and nobody can see anything, behind its own coins, then it created some need, to show those people, that things can be traced, and that they should be more careful, when they make their payments. Note that block explorer for Monero would be much less useful, than for Bitcoin.

A block explorer was eventually born to tag and identify transactions without depending on the Core Software.

If you are a user, then you don't need a full node, to use it. However, if someone wants to run a block explorer, then that person needs it, also because different nodes can have different mempools (and sometimes different blocks, until they are reorged).

you want to own a piece of history by owning a piece of Satoshi or Hal's sats, would you not?

Not really. And mining a lot of coins in testnets, clearly showed me, why it is the case. Every time, when one of my addresses is publicly connected, then I cannot use it anymore, and I have to switch into a different coins. And the same is true with coins, received from signature campaigns: I never know, how many people would explore my history, so I always assume, that every time, when I move those coins, it is obvious, that they are owned by me. In case of test coins, it is easy: they are worthless, so I can just give them away (and call it: buying some anonymity). In case of mainnet, I usually deposit them somewhere, to then withdraw, at a different time, on a different end, or even as a payment to somebody. Because for someone, it may be valuable, to "touch vjudeu's coins", but for me, it is just some lost anonymity, and turned into pseudonymity.