Exchanges are not part of the bitcoin world, they are bridges to it.
Longer version of the above remark: what bitcoin is truly about is financial sovereignty, or, to put it in more layman's terms, lack of counterparty risk. The bitcoins held in a bitcoin exchange are mismanaged funds, you should never leave your cryptofunds in the exchange: "not your keys, not your coins".
PS: These days, you can even find "bridges", i.e. exchanges, that don't have even this problem anymore, e.g. HodlHodl exchange, which doesn't hold customer's funds, so it's impossible to achieve a fractional reserve malpractice.
Similarly, there’s no fundamental barrier to promising to pay someone bitcoins later that you don’t currently possess. That’s the seed of a credit-based economy, and also the piece of the fiat system that makes things so complicated. It is disingenuous to make a comparison that includes this complexity on one side but not the other without giving justification.
You cannot bring points against bitcoin which actually happen more in centralization-backed entities than in decentralized scenarios.
In fact, the least problematic time in terms of bank runs appears to be the years of the highly-centralized Bretton-Woods system post-WW2 (1).
It’s also not like holding bitcoins yourself is entirely risk-free. You can accidentally expose your private key and have your money stolen or you can lose your private key and have it locked away forever. Either scenario means you no longer get to use your money, and any defense against one makes the other more likely; it’s a difficult balance to ask people to get right.
Due to fractional reserve banking, banks lend money they don't have. Banks are only required to have 10% of the money they loan on reserve.
Other than it being too young and inconsequential for people to bother, what property does bitcoin have that works against this scheme? Banks have worked this way since long before modern fiat currencies were developed, and they’ve always increased the money supply without minting new coinage. Whether it’s gold bullion, federal reserve notes, or bitcoin keys in their vaults doesn’t seem to make much difference.
Why with cash many don't do that, beats me. According to Keynes, people should withdraw their cash when there is no interest to be gained ("liquidity trap"). In practice, people don't, and that makes Bitcoiners crazy: good marketing makes (especially badly informed) people act uneconomically, since they think they are saving, while they are actually investing in an indifferent manner.
Other important aspects of Bitcoin are, that it makes the money supply transparent, and everybody can validate transactions. This is not as simple with cash or gold.
The banks provide a service that has some intrinsic value: They protect your cash better than you can, and store it in a place that is physically separate from your home.
Home thefts occur with a higher frequency than bank thefts, and someone who's known to keep large quantities of cash in there home becomes a bigger target. If your money is stored in a bank, you're more exposed to a banking system collapse but insured against ordinary theivery. If your home is destroyed, then your money is still safe; if your bank goes bust you still have your home (or at least the things inside it).
In this case you have to pay a small fee, but you decrease the amount of cash that can be used for loans, and thus make loans more expensive, leading to better rates for lenders in the future. (At least this is my understanding at the moment - still getting into the topic, so please excuse if I am oversimplifiying.)
Most money (specifically, most US dollars) are not in the form of coins or notes. See: https://www.quora.com/How-many-dollars-are-there
~1.4 Trillion USD in notes ~60 Trillion USD total
coins are certainly less than notes, but I'm not sure how much less, so let's guesstimate no more than 0.5 Trillion, and that's a stretch. So, about 97% of money is not in notes and coins.
And it’s the credit that’s making things complicated, not the central banks.
Mtgox was a private enterprise that was managed by incompetent/malicious individuals, why does this always come up in bitcoin discussions? Mtgox is an example why you need to care about owning your money. People who lost money in mtgox didn’t own those money, they gave them away for a promise to have them returned.
Money as understood by economists is not physical currency (coins, notes, etc), but an emergent property of the institutional use of IOUs of various kinds, like debts and fractional reserves. These also exist in the bitcoin world, and have already caused problems— How long did MtGox operate without reserves? Does Bitfinex actually have the reserves it claims to? If Bitcoin were immune from the problems of fiat currency, these questions wouldn’t even make sense to ask.