The areas of law are oversaturated with attorneys

In my opinion, I can't answer that, because "oversaturation" is probably due more to geographical distribution than to areas of practice.  For instance, back when Nevada advertised itself as the state where you could get a divorce after a six-weeks residency period, family-law attorneys in Nevada probably had as much work as they could handle.  Eventually other states began to change their divorce laws.  So married couples were still getting divorced, but in their home states.  With fewer clients, it's possible that some of Nevada's divorce lawyers either had to go into other areas of practice or move to other states.

But I'll tell you what areas will be saturated if the United States ever institutes single-payer national health care, aka Medicare for All.  We won't need so many attorneys who specialize in personal injury and workers' compensation law, either on the plaintiff or the defense side.

Right now, employers are responsible for paying for their employees' work-related injuries and illnesses.  People turn to personal-injury attorneys after they've been injured by someone's negligence, e.g., due to an automobile accident.  Or their own insurance companies are finding excuses not to pay claims.

But under Medicare for All, everyone who needs health care, no matter why or whose fault it is (if anyone is at fault in the first place) will receive it, no questions asked.  Attorneys could still sue to recover lost wages, loss of consortium, and other non-medical damages--but there would no longer be any need to sue for payment of medical damages.

The so-called tort "reform" movement is nothing but a cover for big business, big insurance, and sometimes big government trying to shirk responsibility for their negligence.  Read tort-reform propaganda and you see the epithet "greedy trial lawyers" over and over (when they say it aloud, it sounds like one word), as if lawyers are the villains.  They're not.  Rob a convenience store?  Go to jail.  Market Thalidomide and kill or cripple unborn babies?  Give an unelected bureaucrat the authority to poison the water supply in Flint, Michigan?  Well, whaddaya expect, stuff happens. 

If they were interested in true reform, they'd be marching in the streets for Medicare for All.  The day it's introduced is the day half the law schools in this country will close their doors permanently.

Morever, It varies according to the local market and area of law, and I can't speak for all of them. But family law generally is saturated. There are many reasons for this. First, law schools are churning out graduates who see family law as an easy area to get into, although most quickly find out it is far more complex that it might seem. Second, family law attorneys face competition at the lower end of the market from document preparation services and law firms that provide limited services for a low flat fee. Third, more people are choosing to handle family law matters without an attorney because they feel that they either cannot afford or do not need one. Finally, many younger people are postponing marriage and child bearing, leading to fewer divorces and child custody disputes. I don't see any of these factors as signs that family law is becoming obsolete or even less important. But I do feel that family law attorneys need to try harder to differentiate themselves and demonstrate their value. Gone are the days when people simply assume that they need a family law attorney.