In terms of the way it works, cash is very much not the correct analogy, too.
Transaction wise, cash transactions happen both live and physically, meaning you have some means to make sure the counterparty honors their part of transaction. Electronic cash systems involve third party to coerce the counterparty or refund you. In Bitcoin world, apart from hopes and dreams and magical reputation, there is literally no way to stop the counterparty shoving you their Prodeum. Bitcoin removes the trusted third party of electronic cash, but fails to introduce physical measures of physical cash.
Bitcoin transactions are hardly even transactions, more like throwing money into numbered bin and hoping for the best. To be fair, the system has not gone down the drain once some form of market formed, so the hopes mostly did not backfire. The absence of full transactions in my opinion (I may be wrong, though) means Bitcoin IOUs cannot exist and with that whole financial products market, for better or worse.
Loss wise, cash is either in your posession or not and a lot of times can be recovered when lost. Stolen private keys can remain dormant for indefinite amount of time until they are actually used to move coins to a different address. With cash that one has in their immediate possession it would be immediately obvious if someone tries to take them away. If physical cash bills got sticky, you have taken an extra bill, dropped it on a counter and noticed your mistake, then you can still take back the extra bill. If you have transferred too much/many coins, then it's SFYL. Forgetting a wallet with physical cash somewhere can be SFYL, can still be recoverable if no one took possession of it. Losing access to private keys is permanent SFYL.