I would argue that exercising such leverage is not only for benefit of the indispensable but also for the organizations which are often inert unless enough initiative is given.
Indispensability (true or perceived) hurts not only person but organization as a whole. It creates tension between them, which might break at any point for any reason (a bus, reaching point of no return, dragging organization down) and create difficult to fill void once that happens.
I think it should, however, be considered from the true indispensability and not the perceived one. Perceived one is bullying employees, accidentally or on purpose. Sometimes it's bullying ourselves by creating overly controlled environment that solidified over years.
In perfect life scenario utilizing leverage would work as following: The Indispensable ask for a minor raise (1-5%) -> Company agrees, because The Indispensable is truly indispensable -> 1 month passes -> Repeat
After couple iterations there would be a break point because company will start to weight options and might decide to compensate instead of waiting for next month and another raise request. In this scenario The Indispensable stops being one, so their quality of work improves (less stress) and they get additional income. Company retains The Indispensable since they signaled and through adequate pressure achieved the goal. Fragile process with single point of failure is resolved with more stable solution.
Unfortunately it doesn't work in real life often. Some companies simply can't afford matching expectations, no matter how warranted they are. Indispensability there is simply a tax imposed on worker. Some people aren't confident and courageous enough to bring issues out and try to act on them (as business can be intimidating). Last and not least - true indispensability isn't black or white. There's a mixture of politics, perceived indispensability, true indispensability and controlling behavior by The Indispensable one.