Systems with three central defenders are chosen for a specific arithmetic reason. Against most attacking setups, the third defender is not marking anyone, and that free player changes what the defence can do.
The spare man exists because attacks are narrow
Most teams attack with one or two central forwards. Three central defenders therefore produce a numerical surplus in the middle of the pitch.
The surplus defender is not tied to an opponent, which allows him to cover behind his colleagues, step into midfield, or carry the ball forward.
That freedom is the whole argument for the system, and it disappears the moment an opponent commits three attackers centrally.
The free defender becomes an extra passer
In possession, an unmarked defender is a guaranteed outlet, which makes building against a two-forward press considerably easier.
He can also advance with the ball until an opponent steps out to meet him, at which point the space that opponent left becomes available.
This is why several teams have moved a midfielder into the back line, since the role rewards passing and carrying more than defending duels.
Width becomes a wing-back problem
Three central defenders leave nobody occupying the touchlines, so the wide players must cover the full length of the flank in both phases.
That demand is physical rather than technical, and the availability of two players capable of it is often what decides whether a coach can use the system.
When a wing-back is caught high, the wide centre-back must cover across, which is why those defenders are usually the quickest of the three.
The system is vulnerable to a specific attack
An opponent who attacks with two wide forwards holding width and a striker occupying the middle removes the spare man by matching numbers.
The wing-backs are then pinned deep, the shape becomes a flat five, and the team defends with numbers but attacks with almost nobody.
Teams that face this frequently respond by pushing a central defender into midfield in possession, restoring the spare man in a different area.
It changes what the midfield has to do
With three defenders behind them, central midfielders can be more aggressive in stepping towards opponents, since the cover behind is already established.
That aggression is where much of the system's defensive value appears, rather than in the back line itself.
A back three whose midfield does not press ends up as five defenders watching the opposition circulate, which is the version of the system most people criticise.