The claims (e.g. the bitcoin balance for each client account) is accepted by bitcoin users as a substitute to bitcoin, because when any single client withdraw bitcoins to pay others, they will get bitcoins corresponding to their account balance, so they think that their bitcoins are safe in my storage service, those claims are real
This is not true. There are counterexamples from both sides, there are both claims that do not act as a part of the money supply (e.g. liquid credit that is not issued by banks), as well as components of the money supply that are not redeemable in the base money (e.g. some complementary currencies such as mutual credit). The substitutiveness does not lie in redeemability, but in the behaviour of market participants with respect to it (whether they use it as a medium of exchange and a final means of payment).
But, if more than half of them (or some big clients) withdraw at the same time, that claim will show its fake nature: I don't have that amount of bitcoin to pay them all. Anyway through maintain loaned ratio, I can make sure 99.99% of time there will not be a liquidity problem, that is the nature of FRB, more like insurance, has nothing to do with money creation, I don't need to create any bitcoin to do FRB
It is true that too much withdrawals cause problems. But that does not address the question of the money supply.
Seems that you still have the impression that private banks create money, but if you have read that article I mentioned before carefully, it listed many strange illogical things if that is the case:
It seems that you have what is essentially a non-economic theory.
1. They will be counterfeiting money (US constitution Article I, Section 8 prohibit any entity other than congress to create money)
This is a matter of interpretation, it is up to the courts to determine whether some act is counterfeiting or not, and they decide based on historical context rather then deductive reasoning. Theft is illegal for example, yet courts do not oppose taxation, they just interpret it differently.
2. They will create money and lend to each other to solve their own liquidity problem thus there will never be bank failure
As I already explained, commercial bank loans are not accepted by the market as settlement of their own debt. This is simply an empirical issue, not all components of the money supply are accepted by all market participants in all situations. Just like google nexus is typically accepted on market as a tablet, but if you need an app that does not run on android, you will demand an ipad.
3. Since all the digital money is convertible to paper notes, there will be huge amount of printing activities in treasury when they create new money, since part of those money will surely be converted to paper notes
Currently, people mostly prefer to store large amounts in bank accounts rather than cash due to transaction costs. They do not redeem it just because they can. Redeeming would increase their transaction costs. But when they, for example, lose confidence in banks, they risk of insolvency might outweigh the potential savings in transaction costs, and their preferences with respect to the individual components can change. This causes a bank run and liquidity problem at a bank. This is an empirical issue, and an example when the composition of the money supply changes: market participants stop viewing a component as a close substitute to money, it ceases to be a part of money supply. If there are not enough reserves to cover the withdrawals, the money supply shrinks by the uncovered amount.
4. They will fail to pass double entry book keeping
As I already wrote, the debit component of the loan does not act as a part of the money supply, whereas the credit component does. This is again an empirical issue, people accept the credit as equivalent to money.
Your approach fails to explain the concept of the money supply, to you it is merely an arbitrary legal and accounting concept with no practical application. But this is irrelevant for an economic analysis. The economic concept of the money supply reflects the actions of market participants, what they use as a medium of exchange and final means of payment, not what a judge or an accountant thinks about it. Furthermore, the components of the money supply are not perfect substitutes, which confuses you, because it leads to not all of them being usable in all contexts as money.
TLDR:
- money supply is an economic, not a legal or accounting concept
- composition of money supply can change over time as a reaction to changed user preferences
- the components of money supply are typically not perfect substitutes, just close enough