Adverse possession was never really about squatters' rights. It effectively acts as a statute of limitation that cuts off the period in which someone can make a claim to property based on defects in the possessor's title. It's not about protecting the ability of a poor farmer or poor shop owner to take over some abandoned land. That's the exception, not the rule, and it usually would have happened umpteenth transfers in the past if it happened at all. Usually such people buy the property in relatively informal deals--at least, informal by the standards of the Civil Law, but often sufficiently formal to meet Common Law requirements. But because the risk of title defects is much more ominous in Civil Law countries, banks and other formal sectors of the economy heavily discount the value of that property as collateral, if they even value it at all. So it makes it more difficult for the poor to build wealth. Even in the U.S., many small business owners will get their start by mortgaging their homes. The ability to use property as security is a critical mechanism for the poor and working classes to bootstrap themselves into the capitalist economy.

At least, that's the argument in "The Mystery of Capital: Why Capitalism Triumphs in the West and Fails Everywhere Else" by the Peruvian economist Hernando de Soto. AFAIU, in the intervening years many countries paid heed to his argument and instituted at least minor land reforms, for example making it possible to register transfers where prior records are defective or absent. But unless such reforms are self-executing (as with adverse possession or more modern statutes of limitation), I doubt such reforms are helpful in normalizing the informal property market.

De Soto also makes the case that so-called squatter's rights were an important factor in the emergence of the American middle class, but that has little to do with adverse possession and more to do with rules set by the Federal government in land grants and when dealing with squatters on Federal land. Common Law adverse possession could never operate against the government without their consent.

In modern America adverse possession usually comes into play in disputes over boundaries. A registered property line may have been two feet to the east, but for whatever reason a neighbor has been using that two-foot section as their own for many years, as probably previous neighbors did. When the error comes to light (e.g. maybe the registered title owner wants to build an extension to his house and hires a surveyor), adverse possession is used to settle ownership with the neighbor who has been adversely possessing the strip of land. That's a far cleaner solution than, e.g., an easement, which would just add unnecessary complexity to both neighbors' titles and invite future litigation by subsequent purchasers.

On a similar note, I've read that clearing land to graze cattle in the Brazilian jungle primarily is for laying claims to plots of land purchased formally and informally, rather than for meat production. The presence of cattle is a de facto, and to an increasing extent de jure, proprietary claim on a piece of land. In a sense it behaves very much like adverse possession--the presence of cattle prevents someone else from using the land, given that fscking with someone's cattle can be a shooting offense (like in the American Old West). Some have argued that if there were more convenient ways to secure a claim on land, there would be less pressure to clear cut the jungle. Though, absent concrete evidence that alternatives would lead to less clear cutting, that sounds more like a libertarian talking point designed to appeal to liberals.