Say you buy a theoretical 10 year zero-coupon bond with a 5% yield and a face value of $1,000. You should pay about $614 for it. You intend to hold it to maturity.
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.