With a peg to the USD, banks will be happy to take your real money and hold onto it while the exchanged Berkshare remains in distribution, because they know tha

With a peg to the USD, banks will be happy to take your real money and hold onto it while the exchanged Berkshare remains in distribution, because they know that at worst they only have to pay back the original money. But as soon as the Berkshare is able to move against the dollar, participating banks assume some risk because they may be forced to pay out more than 1 USD for a single Berkshare. There's even some risk that the bank could run out of "foreign currency reserves" (USD deposits) to defend the Berkshare, causing it to collapse.