A distinction between held to maturity assets and market priced assets makes sense though, there should be some consideration in the calculation about term though for sure. The question of that though seems very complex to answer.
Further: the "market value" thing here is complicated. The reason there is separate available-for-sale and held-to-maturity accounting for bank assets is that, in the ordinary course, the assets are held --- the only reason you sell them is because of extrinsic distress. There isn't anything wrong with the agency MBS portfolio SVB had; they're worth less because if you have to sell them in Q1'2023, they compete with even more attractive bonds and are discounted accordingly. But if you just hold them, they pay back dollar for dollar, and that's what the bank normally does anyways.
Granted, it's sometimes hard to establish market value. In the case of assets with genuinely low liquidity, the market value is somewhere above the bid and probably below the ask. Accounting in this case comes with error bars, but it's not really justifiable to approximate the value of an asset outside of this range.
Here's an example. Suppose a hypothetical bank receives 100 dollars in deposits at an interest rate of effectively 0. They use 85 dollars to buy a bond that matures in 1 year that pays 90 dollars, and keep 10 dollars in cash as reserve requirement. They pay themselves the extra 5 dollars as bonuses. They have met their fractional reserve requirements, and according to your scheme, their holdings should be valued at 100 dollars. Are they solvent?
All bonds get held to maturity by someone (unless they default, but that's not the problem here). The FMV of the bond is determined by the value of the bond's remaining cash flows to that person; so if the FMV went down, then that should be a clue that value was fundamentally lost, regardless of who's holding the bond.
Interest rates take a random walk from now until maturity.
Under fair-value accounting, the balance sheet value starts at fair-value (obviously), then gyrates, but tends towards face value, and reaches it at maturity, due to time decay of bond premium. As you said yourself, every bond eventually matures in the absence of credit risks and fair-value can't indefinitely diverge from face value.
Under amortized cost basis accounting, the balance sheet value starts at fair-value but then increases every year until maturity, at which point it is also face value.
Surely you acknowledge that these are the same? They both describe the exact same cash flows.
That's the loss that took down the SVB, and it's a real economic loss. If the SVB's depositors behaved like the simplest textbook model, then as soon as short-term Treasury rates increased, they'd insist on correspondingly increased interest on their deposits. The cost of that extra interest would be the SVB's loss--the cash flows in from the bonds stay the same, but the cash flows out to the depositors would need to increase.
In reality, I understand that depositors are generally "stickier" than that, leaving their funds at their existing banks even when bank interest rates increase slower than Treasury rates. That gave the SVB some hope that they could earn their way out of the hole, passing the loss slowly to their depositors over time by paying below-market interest rates. That's the behavior that HTM accounting roughly models. The SVB's depositors had no economically rational incentive to accept that though, and they didn't.
... but SVB expected to have positive net-interest-income with increasing rates. Look here:
https://www.sec.gov/Archives/edgar/data/719739/0000719739230...
A 100bp increase in interest rates would've increased net-interest-income by 1.8%; a 200bp increase by 3.5%. This is typical for banks, because lending rates go up more than deposit rates as the base rate increases, increasing interest margin.
So the idea that this is about NPV of future cash flows is not right.
Of course most of the money left in a self-sustaining bank run, not directly for the reason above. There's a quite rational reason for someone to start that run, though. That reason wouldn't exist if the bank were well-capitalized on a MTM or NPV basis.
The SVB's expectation in that 10-K is a model of depositor behavior, predicting that depositors will leave their funds at a MTM-insolvent bank earning below-market interest for long enough for the SVB to earn its way out of the hole. That prediction obviously didn't come true. So doesn't that just mean their model was wrong, and shouldn't be relied upon elsewhere either?