It's a good idea for future satellites, but upgrading existing satellites is probably not feasible.
And these polar orbit satellite typically live a lot longer than the relatively short lived starlink satellites, potentially opening you to a (perhaps unlikely?) scenario where starlink moves to new and incompatible hardware for inter-satellite communications, and your satellite is then made obsolete.
Vertical integration is not cheap, but it does have it's upsides.
That would require replacing all the satellites with new ones capable of doing that, which doesn't seem feasible. Starlink also doesn't have great coverage of the polar regions.
“We're passing over terabits per second [of data] every day across 9,000 lasers,” SpaceX engineer Travis Brashears said today at SPIE Photonics West, an event in San Francisco focused on the latest advancements in optics and light. "We actually serve over lasers all of our users on Starlink at a given time in like a two-hour window.”
Again though, you can't do "Starlink from the satellites, so we don't rely on a specific ground station" unless all of the satellites support talking to Starlink, which they don't. That means they'd have to be replaced.
As I understand it, the Starlink network has a number of ground stations, and an active inter-satellite "mesh," thanks to laser links, which would allow it to route around the loss of one or more ground stations? (although obviously it requires at least one ground station to be live in order to access the non-Starlink-connected Internet)
The lasers began being integrated between 2020 and 2021, so it's likely SpaceX has made decent progress equipping their network with this capability, although I can't find the latest figures for the proportion of satellites that have lasers.
It sounds like there's something I'm missing if we can't do "Starlink from the satellites, so we don't rely on a specific ground station"