I'm from a similar background and this doesn't make any sense, but since I know it's going to devolve into an argument of "Well, they don't speak the primary language in the area, so they can't communicate with the tellers", "they're too old so they can't drive anymore", or "they're illiterate [either literally or financially] and their caretaker doesn't like taking them to the bank", I'm not going to go there.
I'm not saying people with unique issues shouldn't be accommodated, but their problems are more basic than something that a change in bank policy/regulation will adequately improve. The issue is not about being "underbanked", it's about improving accessibility to the environment.
It is true that at a time in the past, checking accounts were guarded more carefully, as the bank was fronting that money on your behalf and would have to be reasonably confident that it'd be in your checking account when they went to get reimbursed. That's not unreasonable, but checking accounts weren't the only type of account offered at the bank, and they absolutely were in wide use, even among unfortunate people, at least until they bounced too many checks.
This has mostly gone away with debit cards, because the bank can now tell whether you have the money in the account or not before they approve the transaction. Last time I got a checking account, the process was a formality, and there were no eligibility requirements in excess of the documentation legally required to open an account and the (small) minimum deposit.
The other thing is there's an implication here that banking is a human necessity. There's another commenter who laments that people in Nepal don't have a Mastercard.
People do not have a right to banking. It's a private service, and in many ways (described above), it's not a desirable one. Banks no longer pay an appreciable amount of interest, which was most of their value proposition to the consumer before they were able to shoehorn in as the keepers of electronic payment systems.
I'm just going to call a spade a spade here, and say that the reason there's a sudden interest in the "unbanked" is that they have a harder time participating in online commerce, and the government is anxious to hop on board that train because money in banks is money under their control.
Some founder of an irrelevant SaaS app is lamenting that a Nepalese person may not find it convenient to pay him $10 / mo to email the local air pollution index or something. That's a pretty silly thing to try to cause a moral panic over.
If we want to talk about how it's cool that Amazon has devised an electronic payment system that circumvents banking, that's great, I think it's awesome. But I'm not on board with the terms "un[der]banked" in the first place, as they imply that banking is a default, and then if we accept that, I'm still not on board with acting as if they are signals of some meaningful social malignancy.