Part of the problem is going to be an overcapacity issue. The most obvious is the duplication of capacity caused by the Chinese and US constellations. It's safe to assume each country isn't going to permit ground stations or terminals from the other.
One possible solution is permitting some sort of version of internet peering or transit. The constellation owners make some sort of deal (blessed by their respective governments) that allows encrypted data links between satellites and ground that are only decrypted once they have reached an approved decryption gateway to the internet.
For example, a Starlink terminal in the US might link to a Chinese satellite using a Starlink account. The Chinese satellite links to a Chinese owned ground-station (maybe in the US, maybe not). The ground station connects to the approved gateway (much like an IPX). In theory, the Chinese portion of the network can't tell what the data is, but now Starlink can get by with fewer satellites. And visa versa.
Obviously you'd restrict such links to only non critical stuff. For example, nothing national security related.
Basically a satellite equivalent to internet peering that avoids every company needing to run fiber from coast to coast.
But I don't see this happening any time soon.