The total long-term value of bitcoin ecosystem is the value of bitcoin as a transactional instrument.
There's a plausible justification to invest in bitcoin now if you believe that in future it'll have a large total capitalization because be used as valuable information of e.g. uncensorable pseudonymous transactions, and you'll be able to sell your bitcoins with profit to those people who'll want to use them for transacting.
However, it's not reasonable to state that the valuation is justified by it being used solely as a savings/investment vehicle; because what is the future exit for that investment? When a number savers in aggregate decide to withdraw their savings from the ecosystem at some point (which is inevitable, the global economy has cycles and at some point people will want that), to whom do they sell bitcoin? If there's a different use (as the one described above), then that's an exit that will set the total value of bitcoin at such an event; but if the only use case is "decentralized savings" then it's comparable to the "greater fool" motivation, you can sell/withdraw while there's someone else who wants to enter the product, but when the aggregate motion switches from saving to withdrawing, the value suddenly drops to zero - exactly the behavior that should be impossible in a good savings (as opposed to speculation) vehicle.
I like to think of bitcoin as the censorship resistant settlement layer on which payment networks/systems can and are being built (like lightning network, which just passed all tests). There are some pretty sweet video demos of lightning network/payment channels in action.
Don't forget that it's now possible to broadcast bitcoin transactions via satellite - without internet...
That could very well be the thing, and there's certain value in that, however IMHO that value is limited because:
1) the market value of a settlement system handling is much, much lower than that of a retail payment system with a comparable value (not number) of transactions. If the "payment of the future" is a side-chain that uses bitcoin as the settlement layer, then that side-chain will be the value creator and get almost all benefit of that value, not bitcoin. Offering payment services to consumers and businesses is a huge value proposition; offering settlement services to institutions or technological payment networks is a lot of value as well but there's less market lock-in and network effect so that's going to be much more commoditized and more vulnerable to competition with established channels.
A consumer is only going to use a few payment methods for convenience reasons; a sophisticated institution (no matter if it's a bank or simply a large corporation selling stuff) or a realistic payment network is easily going to use all possible ways to settle their debts with institution B and is going to route every transaction among the cheapest route possible for that deal. Currently bitcoin is order of magnitude too expensive compared to other real time gross settlement systems (e.g. Target2 starts with ~dollar per transaction and becomes cheaper with more volume), so only transactions that require censorship resistance would be settled through bitcoin and all others would not. Even if we're not talking about institutions but a purely technological solution, using bitcoin as the settlement layer is something that can and will be switched to a different layer if that's more attractive.
2) The properties of bitcoin (irrevocability, pseudonymity, censorship resistance) are benefits to many consumer use-cases and markets, but not particularly relevant to large-volume settlement systems. Anyone who has thousands or millions of payments to aggregate and route through a gross settlement system would generally prefer revocability (partners of payment networks explicitly designed revocability in the protocols they designed, because they wanted this feature); they don't care about pseudonymity because they're large enough that they can't hide, and they don't care about technological censorship resistance because they anyway can't advertise/sell their services if they violate that censorship - they're too large to hide, and they'd be visited by angry men with guns if they tried that. Settlement layer has an entirely different target audience than consumer payments, and that audience has entirely different needs - ones that Bitcoin doesn't fulfill particularly well.
I.e. bitcoin can be used to, for example, smuggle capital out of China avoiding capital controls, and there's value in that use-case; but if it's used as a settlement layer for a service or process smuggling capital out of China, then that wouldn't drive up/maintain the price of Bitcoin nearly as much, and having a censorship-resistant settlement layer doesn't enable you to offer censorship-resistant payments unless all your other money flow is also censorship-resistant.
This was addressing the parent poster's proposal of a single, quite particular (and IMHO not in popular opinion) use-case of it purely as the settlement layer for other payment network(s); but there seems to be no consensus about the main use case, at the very least I see camps of 'value store', 'decentralized payments for the masses' and 'payments that can't be restricted' which already each have some conflicting requirements.
Debt-fueled inflation resistant money. It is right in the statement in the genesis block detailing a bank bailout.
https://en.bitcoin.it/wiki/Genesis_block