I've never seen such a sign, but I'll take a guess what it might be referring to. Here in California, the definition of a freeway does not have anything to do with number of lanes, speed limits, the presence of freight traffic, or any affiliation with the National Highway System. Instead, it is defined in the California Vehicle Code section 332 as:

a highway in respect to which the owners of abutting lands have no right or easement of access to or from their abutting lands or in respect to which such owners have only limited or restricted right or easement of access.

This roughly corresponds to what the Wikipedia describes in its page on "controlled access highways", a term which includes the California and USA federal government's term of freeway or the eastern US states' term of expressway or the British motorway. That is, a road which all ways onto and off of the road are carefully crafted.

There are many roads in California and the United States which will meet the requirements outlined by the Interstate Highway standards, and will look and feel like an interstate freeway, from the signs and lane markings and shoulder sizing.

But none of that matters for the California legal definition of freeway. Indeed, some freeway-looking roads will have signs that say "end freeway" or "start of freeway" with no other visual cues. And this is because the California Department of Transportation (CalTrans) has not acquired the property rights from adjacent landowners to prohibit building driveways onto the public right-of-way.

To clarify, a right-of-way is not an individual right like free speech or freedom against unreasonable searches. Rather, it's a legal term referring to a property right, namely a grant of access on/over some piece of property in order to cross it. In the case of public roads, the property right is held by a public entity, and that means the public can use it. Since a right-of-way is a type of property, there are rights implied by a right-of-way. So a right-of-way right. Yeah, lawyers named things badly here. Anyway...

A feature of public rights-of-way is that any adjacent private properties can connect to and travel upon the right-of-way. The rationale -- to oversimplifying things -- is that if the public entity could deny the right -- including to build a driveway -- then a property could end up with zero ways to access it without trespassing, making it impossible to enter or exit, which makes the property near worthless. It is an age-old rule from English Law that rendering property worthless is bad, so private property rights necessarily comes with an implicit ability to connect to adjacent public rights-of-way.

But property rights are a bundle which can be sold separately by their owner. For example, many suburban property owners don't own the rights to minerals underneath the land, since the preceding developers sold that right to someone else. And so the state -- through CalTrans -- or the city or county can buy (often through eminent domain) just that single right from the property owners. Thus, the properties along a road might -- unnoticeable to the naked eye -- not be legally allowed to build a driveway, having shed that legal right away by forced-yet-fully-compensated sale.

To that end, it's possible that a sign warning against illegal driveways is the state's way of preventing future land owners from trying to build such driveways, since those owners would lose in court. If the state has acquired such rights, it's usually because the road is planned to become a freeway or expressway (a limited-access road, in California terminology), or they wish to preserve that possibility early and for cheap. So far as I'm aware, in California the right is only ever acquired for state roads, with the sole exception of the expressways in Santa Clara County, because they planned well ahead in the 60s.

Other states may be similar, by extrapolation.

TL;DR: OP's state might be hedging their bets to build a future freeway, and wants to prevent future legal issues with landowners, since the state knows it would win those cases

Others have answered why it is a law. But why does it need a road sign? You haven't talked about where you live, but I assume it is a rural place that is slowly suburbanizing by people splitting their property into smaller parcels and building on that as the paperwork is generally easier and that form of density is baked into the zoning of the area.

The problem with this type of building over larger subdivisions is that the road network usually isn't as developed, since a developer isn't building the internal road system nor possibly paying for improvements to nearby infrastructure. You also have less experienced developers, generally. Many times, these can be the home owners building themselves and sometimes acting as the general contractor. These smaller future home owners may not be aware of all the paperwork required to develop their property.

Where I live you can't simply bring a driveway out to the road. You have to get permission from the township and pay for access. They come out, install a culvert, install a blue 911 flag with your number on it, and build a driveway connection to their standards. It costs several thousand dollars.

It’s probably the end result of a Republican controlled legislature enacting laws to regulate nonexistent problems—I’m sure some state rep had a friend who owned a sign vendor so he pushed through a local ordinance requiring signage to declare that you can’t drive onto a road, all sold as blocking “illegals” from “getting drivers licenses.”

ppl like me who dgaf and just drive through the ditch

I have also wondered this for years! Googled it once, and found bupkis. Really hoping someone here has an answer!