It may seem ridiculous to let a civilization expire, but what would the ramifications, galaxy wide, be?
So should we allow a toddler who wonders out into traffic to be hit by a bus because they could be the next Pol Pot?
In TOS the Prime Directive was about not-interfering in the development of a race. That means not introducing technology or solving their problems for them. They have to do that on their own. They have to find their own way in that regard. Even then, the Prime Directive had stipulations, the culture had to be living and growing. If that growth was stunted, a captain could make a case for interference. Also, the Prime Directive didn't seem to apply when a culture presented a hazard to their neighbors. Or after prior contamination.
Let's also be clear that even the writers of TOS weren't sure of how they felt about the Prime Directive. In "Assignment: Earth" (written by Gene Roddenberry), we see an organization charged with making sure Earth doesn't destroy itself before reaching its potential. In "The Paradise Syndrome", we see the Enterprise diverting an asteroid from a planet with a small, underdeveloped population. There is no mention of it being a violation of the Prime Directive. In Voyager, we know there are 47 subsections of the Prime Directive and even an Omega Directive that suspends it.
Picard interpreted the Directive correctly in "Symbiosis" because the issues were part of their societies growth. Every other time (it seems) the only time Picard would interfere was if he had a personal stake in the situation.