Did we ever consider what Satoshi insinuated by "cash"?
...
It makes sense considering his design of the system that Bitcoin can not ever reach the ubiquity of cash in transactions worldwide. This would necessitate such as scale as to effectively centralize Bitcoin and therefore defeats the original attempt to remove trust
.
Perhaps not as ubiquitous as cash transactions worldwide, but it is crystal clear from the 3rd sentence in the Introduction of the Bitcoin white paper that Satoshi expected Bitcoin to be
more useful for small casual online transactions than Visa, PayPal, etc:

Sure, does he necessarily imply that these should take place on the mainchain or did he not envision (and maybe couldn't at this stage) that Bitcoin would spawn an entire ecosystem that would serve all use cases he describes using Bitcoin as the settlement layer?
The entire paper is about transactions occurring on the Blockchain.
...Maybe we ought to admit that there are intricacies about Bitcoin that Satoshi had no possible ways to know about when he laid the groundwork? I believe nullc was quick to point out a couple of these to you on reddit the other day. Consider for example the 21 million limit which was not specified (and actually not even enforced in the original code).
Satoshi
does mention a limit to the number of coins:

Satoshi does NOT mention a block size limit AT ALL, regardless of what nullc says.