Chequing accounts (non-interest-bearing accounts, used primarily for their other conveniences) are an instance of a bank providing a (traditionally) not-bank service.

Basically, chequing accounts (and all their features: cheques, wire transfers, EFTs, cross-bank ATM withdrawal, etc.) are forms of remittance: a service where a group of people get together and agree to maintain an 'eventually-consistent' balance-sheet between them. Alice goes to one member branch of the remittance group and gives them $N (plus a transfer fee $F) to send to Bob, who may be anywhere else. Bob goes to a different member branch and gets his $N. $N is transferred from the pool to the branch Bob went to to cover their loss, and then $F is split between the group.

Remittance has never really been a function you would expect a "bank" to provide until quite modern times; banks tended to be single-branch, holding the deposits of the people who put them in that bank. You could get someone else's deposits from a bank if they had them turned into a bank note and gave that note to you, but to withdraw it, you'd have to go to that bank. (Greenbacks--federal bank-notes--were a clear innovation from this system. Imagine, a system so bad for holding and transferring value that "cash" is an improvement!)

When a bank temporarily ran out money to cover its outstanding liabilities (withdrawals), it didn't ask to be paid from some pool--it just took out a loan with a neighboring bank. (This still happens, and it's the basis of one of the very important numbers in Macroeconomics: LIBOR--the London Inter-Bank Exchange Rate, which measures the average interest banks will ask for when giving out those bank-to-bank loans, and which is built into the base of pretty much any other loan interest rate you might look at.)

Eventually, though, wire transfers plugged banks directly into one-another's balance sheets in a way they weren't before, and banks could suddenly outcompete all the traditional remittance providers because, unlike the remittance providers, they already had pretty much the whole population of each city/town they served as members. It's like Google suddenly realizing they could do ads when they already had so many eyeballs specifically looking for things to purchase online: it went from "fun idea" to "main money-maker" in the span of a few years.

But that still doesn't mean that that's what it means to be a bank, or that Bitcoin "banks" make any sense. Bitcoin remittance providers, sure--but nobody ever figured it was a good idea to keep their savings with a remittance provider ;)

It's also discounting fractional reserve banking. Banks loan out many times the money you give it. These days 10 time more loans than capital is considered good, 100 times is the practical maximum you see (except in problematic cases, Greece Spain and the like).

That's why most loans specify that you can't withdraw the money into cash. Even 1% of people doing that would be a "bank run" and bankrupt the bank.

"Fractional reserve banking" with a 10% reserve does not mean that if depositors deposit $1M, the bank then lends out $10M. It means that if depositors deposit $1M, the bank retains $90,910 as a reserve and lends out $909,090. That's how the bank "loans out ten times the money it has".

Note that where before we had $1M of "money", now we have $1.91M of "money": the actual money provided to the borrowers, plus the on-demand deposits of the depositors. But the borrowers will probably deposit the borrowed $909,090 in their own bank, which can then lend 90% of it out again. If this procedure is carried out to the limit, you do eventually have 11 times as much "money" floating around the system as the "original" deposit, so the banks in aggregate have loaned out ten times the money originally deposited.

What is this about "most loans"? Generally when I've taken out a loan, the loaned money has been spent in something equivalent to cash rather quickly — generally in the form of a transfer to another bank via cashier's check, but that's equivalent from the point of view of the bank!