The coins are yours, but their value is almost zero unless you exchange them for currency. (Very few places accept BTC directly) Exactly like with company scrips, company credit or such means.
First, we both agree that the market is far from saturated with BTC. When/if it is, then sure many more places will accept BTC.
Second, even with USD you are separating payment processors and issuers. Visa/MC being shut down does not make USD worthless. Just like if some major exchanges disappear, that would only make people seek some other ways to perform transactions they want to perform.