I am very curious as to how much truth there is behind the statement "unregulated nature of space" and especially curious, if true, how long it will be before governments start attempting to
While there is no fundamental reason why governments couldn't create ASAT weapons to reach higher altitudes, the costs go on significantly. Previous (like cold war era) attempts at high altitude weapons pretty much just strapped a big nuke to a full out launch vehicle. For reference, the weapon used by the US in their ASAT kill in 2006 was made using a modified ballistic defense missile (the SM-3). Your Aegis equipped warships can carry a -lot- of them.
Anyhow, it'd be far easier for governments to attempt to regulate the receivers and transmitters than to shoot down the satellite. Also, it would be easier for them to deny launch privileges than wait till after they launch. They might not own space, but they own their airspace.
Anti-satellite weapons were largely held in check by technical issues, cost, as well as avoiding escalation/arms race. The recent weapons test are an example of that. Once you start actively developing these weapons again, everyone else who can will follow to protect their interests. Both of their spins are largely for PR, not legal/treaty reasons.