"Intrinsic value" is a misnomer, intentionally designed to mislead people. The only legitimate use of the term is in futures/options trading as there is a "present value".
Case in point, answer these three questions:
1) What is the intrinsic value of water?
2) What is the intrinsic value of water if you are lost in a desert?
3) What is the intrinsic value of water if you are drowning?
One's answer will always be different for all three cases, indicating there is no such thing as "objective value". In the case of #2, the average person may be willing to lose a limb to avoid dying of thirst. In the case of #3, the average person may be willing to lose a limb to see enough water removed that they could obtain another breath.
Value is always "subjective", no matter what adjectives are added to it. To argue there is some inherent property of an entity that provides an objective value to it, is to purposely mislead people.
Bitcoin is money (or can be used as such) because it is like gold and other precious metals. They are all scarce, which gives them *some* value, even if it's not always a stable one. Even fiat money has scarcity, regardless of inflation, it is not infinite, even if some might be trying to make it infinite even today.
There's an old saying that goes: "Money is a matter of functions four: a medium, a measure, a standard, a store."
Gold and other precious metals have problems with the second of these: measure (AKA unit of account).
A good unit of account has to be divisible, fungible, and countable.
Precious metals meet the fungible and countable requirements, but have struggled over the years with meeting divisibility. After all, suppose you were to do work that is the equivalent of 5.1 grams of gold. The individual you did the work for reaches into their pocket and gives you 6 grams and asks for .9 of a gram in change. How do you provide it?
Bitcoin solves the divisibility problem of scare goods, while still meeting all the other requirements of money.
So if you wanted to say there was any sort of "objective value" of Bitcoin, it would be the following: Bitcoin is a medium, a measure (divisible, fungible, & countable), a standard, and a store.
From there you can argue whether or not it fits these attributes better than fiat money, but it almost certainly meets these attributes at least as well as precious metals.
I agree with most of what you say here, except your description of "intrinsic" as "objective". Intrinsic value, when used in the money domain, means the value that is not echange value. It is not objective by any means, it is defined by supply and demand as everything else.
Imagine that gold is unsellable as a used item, like an opened bag of potato chips. What is the value? You could make things out of it, use it in electronics and so on. A piece of jewelry is nice, but the wearer (and everybody else) is also conscient of its exhange value, so lets take that out. I would say that it is worth far less than the current gold price, driving its use up and the mining down. This is the intrinsic value (intrinsic used in the money domain).
Money is the stuff that is used for indirect exhange. Gold, silver, fiat, bitcoin. The quality of a sort of money is decided by its traits like fungibility, scarcity, divisibility and some others. In fact, the best money has no intrinsic value. Gold having intrinsic value means that its use as money displaces its use in electronics. Imagine food being money - saving would make somebody hungry. Anything can aquire some moneyness, or exchange value, especially in times of hyperinflation or when use of the best money is restricted.
If you don't like the word "intrinsic", which, outside of the money domain, means inherent, fundamental or genuine, use either "direct use-value" or "value apart from its exchange value"
Present value is the value calculated using some future value and some interest rate.