Banks have existed long before fractional reserve though. You really don't need fraction reserve for banks to exist.
How would that work? You put money in a bank, the bank can only keep it in the vault, sitting there doing nothing waiting for you to take it back, unless it can lend part of it out. Thus fractional reserve. Loans existed before banks, but fractional reserve is the whole trick behind banks. Banks started out, I believe, as as goldsmiths[1]. They were places where people paid to keep there gold and and other valuables, and got a receipt for the deposit. These goldsmiths also loaned their own money to people at interest. Eventually some of the more risk taking ones decided that since not all depositors would come for their money at once, they could lend some of deposits out at interest. Modern banking was born.
[1]http://encyclopedia-of-money.blogspot.com/2010/03/goldsmith-...
Well not only would banks be far less profitable, but the entire modern economy would grind to halt. I think that's the real problem with 100% reserve banking--it's disingenuous to cast it as less profit for banks.
We could get rid of almost all the bank default risk by making banks match the maturity of their deposits with the maturity of the loans they make. But with less risk, the bank would not be as profitable most years.