Bill,
You might not agree but this has happened and been upheld several times. The argument made by Associations is that you, when purchasing your property, agreed to comply with specific rules and regulations. If one of those rules were that you would park your vehicle in your driveway or garage and not in the street, then those are the terms of the contract. How that section of the contract is enforced (fines, towing, etc.) would also be in the contract and/or applicable statutes.
What the Association can not do is prevent a non-member from parking on the public street, as they were not part of the contract. However, if they were a guest of the member, most governing documents specify that the member is responsible for the actions of their guests.
Here is some info on the topic:
New Arizona law limits future HOAs’ control of parking on public streets article where an AZ State legislature was so mad when they found out that Associations had the authority to prohibit a member from parking on a public street that they created legislation to stop that from happening in the future.
Can Charlotte HOAs prevent on-street parking? 2013 article in the Charlotte Observer (newspaper)
MARYLAND ESTATES HOMEOWNERS' v. PUCKETT (Missouri) which seems to be referenced in many cases in other States, seems to be the basis for enforcing parking restrictions on public streets on Associations members.
Per
CA Civil Code §1354, The covenants and restrictions in the declaration shall be enforceable equitable servitudes, unless unreasonable. As I understand it, CA courts interpret this to mean that if the parking regulations are in the deed restrictions, then the Association may enforce such restrictions on it's members (but not the general public).