Good question. I'll try to give some of my thoughts on this as an XRP investor:
The main purpose that banks want to use XRP is for fast, international payments. One of the major goals would be an alternative to traditional payment systems like SWIFT. The coin price does not matter for this purpose as FIAT A (e.g. USD) would be immediately converted to XRP and back to FIAT B (e.g. EUR). The process would take a few seconds. A recent test between a Canadian bank and a German one took 8 seconds, compared to the few days/weeks it would take for traditional international transfer. This would solve the liquidity issues that banks face as currently they need to hold vast amounts of FIAT currency all over the world.

While this does not require banks/organisations to buy or hold any XRP at all, the vast majority would want to hold some for the transfer process to work as smoothly as possible. More adoption by banks would lead to both higher market cap and a better case for other payment processes (e.g. international business payments with market FX rate).

Pretty sure that either the Ripple CEO or chief cryptographer explained this in an article somewhere.