There's no concept of airspace in space. You have very few avenues to keep a sat restricted to a geographic region. Orbits like geostationary and molniya exist - but they come with their own limitations for many applications.
The concept of “airspace” is purely a legal one and exits only if your country has an air force able to enforce it (see how Israel has absolute control over Lebanese airspace), any country with anti-sattelite technology could at its disposal could declare that their airspace goes up to the geostationary orbit or even above.
Of course it would complicate the use of satellites a lot, but given their military importance it's likely that this will happen at some point when the tech is ready (by tech I mean a way to stop foreign satellites from operating without causing Kessler syndrome)
There are soft kill mechanisms that can avoid the Kessler syndrome, at least in the beginning. But that isn't the reason why territories aren't defined beyond the atmosphere. It's easy for a plane to avoid flying over another country. But it isn't as simple for satellites to avoid flying over another nation. Orbital mechanics doesn't give you much freedom to do that. Satellites overfly hostile territories thousands of times on a daily basis. If even the countries with soft kill ASAT starts prohibiting that, then spaceflight will become untenable in less than a day. The lack of territorial claims in space is just the world nations being reasonable.
