There are two separate issues here: the government itself being restricted, and the right of the people to collect and disseminate information (in this case, information that is quite arguably in the public interest.)
The government can certainly be limited by statute (police may be statutorily required to obtain a warrant to use aggregated ALPR data or may be barred from using it entirely), and may already be limited by existing case law - the relevant courts have not yet decided.
Limiting Home Depot from streaming a traffic cam or CCTV footage from the confines of their publicly-accessible property is no different than limiting a news crew who would choose to capture the same footage and share it with the world. This is very basic freedom of speech/press - especially when the information isn't being individualized to any one target (as a credit bureau might do.) Everyone is being collected and processed equally.
See: https://en.wikipedia.org/wiki/Sorrell_v._IMS_Health_Inc. - and have a look at the panel of Justices that ruled in consensus, even Sotomayor joined the still-existing majority on this matter. GP's proposed legislation almost certainly runs afoul of this fairly-recent decision.
> There’s obviously a line somewhere though
For the limitation of the government, the line is called "reasonable expectation of privacy." Any reasonable person would expect there to exist reasonable expectation to privacy in a bathroom stall, and the user of the stall has generally taken affirmative measures to ensure the same: they closed the door behind them, locked it.
When you are outdoors, especially on public property, you generally have no "expectation of privacy." See: https://en.wikipedia.org/wiki/Katz_v._United_States
You may be recorded, the things you are observed doing are admissible in court, etc. in places where you reasonably expect people to be able to observe you. Driving down a public, taxpayer-funded road is the quintessential example of "no reasonable expectation of privacy."