What exactly makes it as "bullshit" investment vehicle, as opposed to a good investment vehicle?
I raise this every once in a while on BTC discussions and nobody's ever been able to tell me anything about the investment fundamentals of BTC. Why should it even be worth anything, and why should it go up? Owning (some part of) a BTC just means that you can use the blockchain to prove that a while ago, someone raised the total entropy of the universe by solving a relatively unimportant crypto problem. I fail to see why that (solving an insignificant crypto instance) should be worth money in the first place.
BTC is literally just some bits in a few computers out there. It is not backed by the full faith and credit of a stable entity like the US government, and, because the blockchain is literally a distributed, public transaction ledger, it's more trackable than cash (as another commenter noted. I can't reasonably expect to make significant amounts of transactions with them in day to day life (Bay Area coffee shops that accept BTC notwithstanding). I can't explain it to my mom, which tells me I don't understand it, and nobody else can explain it to me, which tells me they don't understand it.
Even assuming you can answer why they should be worth something, why should these bits be worth more than the output of /dev/random, or some bits that make up a MP3 file?
Money is just information, like music. There is no reason it needs to be slow, expensive, or restricted - which all other money currently is.
Bitcoin is better at organizing the information of money than all other existing methods. This (+ scarcity) is what enables it to be valuable.
Specific bits in the bitcoin blockchain are not valuable, as you're stating. There are no individual bits in memory or on disk that have value. They're simply clones of the same distributed information, which is that you have some slice of the pie. It's your ownership of the slice of the pie that is valuable, because it is scarce, and because it is value-information that is fast, cheap, and global.
What does "backed by the full faith and credit of a stable entity" even mean? Why does it matter? Does it have anything to do with the organization of information? It seems like it doesn't.
I understand it to meant that the country in question will be a currency-recipient of last resort: the country will always accept taxes paid in this currency, and will use this currency to charge for government services and pay its employees. This ensures that there's always a market for the currency -- something that you don't have a guarantee of otherwise, unless the mode of payment has non-financial uses (like rice, cloth, nails, or cows).
"Backed by faith" doesn't exactly inspire my confidence, and the US government is unhinged.
Well why don't you generate some bits from /dev/random and see how much people will offer you for them?
The reason Bitcoin is worth more than arbitrary bits is because it can't be faked (you can't just create more bits for free and spend them again) and because everybody else agrees that they're worth something. The same properties that any system of money requires.
EDIT: And what do you think it means to be "backed by full faith and credit"? It sounds grandiose but is meaningless.
The collective belief in the value of intrinsically useless mediums with certain properties is one of the major technological breakthroughs of humanity. Currency is the bubble that seemingly never pops. Bitcoin and its future incarnations aim to improve it.
Proof of work has nothing to do with giving Bitcoin value. PoW is the cost the distributed network pays for trustless consensus, nothing more.
To understand your fundamental misconceptions, I would start by reading the seemingly unrelated but actually very relevant book Sapiens by Noah Yuval Harari.
Finally, Monero solves the privacy problem of Bitcoin if that's the kind of transaction you want to make, but this is another topic.
In other words, owning a non-dust amount of Satoshis gives you some useful property. Anything scarce and useful will have value and market will price it. Anything with price and good properties to become means of exchange, unit of account or store of value can under some circumstances become some form of money.
Output of /dev/random is not scarce.