While you can generally restrict new ones, you can't eliminate existing ones without basically paying out the lost revenue+etc to whoever is running it.
They have not gone extinct.
I believe regulatory changes similar to what you propose have been ruled takings in the past. That doesn’t necessarily mean that the state would lose, but this supreme court doesn’t seem particularly amenable.
Business & Professions Code § 5412 is the current controlling statute, and that is a codification of what the courts have required.
That requirement is not just a california constitutional problem, but a federal one.
So even if you modified the california constitution, you'd still have the federal problem.
The federal problem is much less than the state one (SCOTUS has found the floor here to be quite low), but it's still bad enough that feds require compensation as well. Just less compensation.
For example, 23 U.S.C. § 131(g) conditions federal highway funds on paying just compensation for removals along Interstate and federal-aid primary highways — 10% of apportionment forfeited otherwise.
I looked into this quite heavily, and had long discussions with legislators, because there was a huge ugly billboard 150 feet from my house in San Jose :)
It's not a government problem - it's a constitutional one - Banning existing billboards is considered both a first amendment problem, and a takings problem.
Doing it without compensation is a constitutional violation, and even if california modified it's constitution, it would be a federal one. Less of one for sure, but still an issue.
The current law (Business & Professions Code § 5412) is a codification of what the court requires.
>Doing it without compensation is a constitutional violation, and even if california modified it's constitution, it would be a federal one.
Only matters if the constitution is enforced. Courts can easily overturn previous decisions. If there's a will, there's a way.