Everyone gets this wrong, cost is not price. SpaceX themselves launch Starlinks at about $1,200/kg but they charge customers closer to $12,000/kg. Do the math. Costs coming down are increases in SpaceX profits, not decreases in customer prices.
Besides what 55555 said, in the near term SpaceX has indeed passed at least some of the cost savings onto customers. NASA administrator Bill Nelson quoted a member of the Joint Chiefs as telling him that SpaceX had saved the US government $40 billion for just launching military payloads. <https://www.fool.com/investing/2022/06/05/did-spacex-really-...>
Over the extremely long term in competitive industries, prices asymptote at ~costs. So it's still a generally useful measure, and in ~all cases, it's at least a directional indicator.
Why would the extremely long term be a useful measure, when we have no way to know how long that will take to happen, and no way to know what will happen in the meantime to disrupt it?