A healthy cat does most of this herself. What you are adding is the part she cannot do, and a weekly look at the skin underneath the fur.
The Cornell Feline Health Center gives two reasons for it that have nothing to do with how the coat looks.
The second reason is hairballs. Cornell notes that fur you take off with a brush is fur the cat does not swallow, so she has fewer problems with them. And the practical one: they say brushing is much easier if you train a cat to accept it while she is young, which is worth knowing before you try it for the first time on a six year old.
A mat is not just tangled fur. As it tightens it pulls the skin up into itself, which is why a cat will object to you touching one long before you have got near it with anything.
Loose ones near the surface can be worked apart with your fingers and a comb, a little at a time, holding the fur at the base so you are not pulling on the skin. A mat that is tight against the body is a job for a groomer or a vet with clippers. Scissors are how cats end up with cuts that need stitches, because the skin lifting into the mat is directly under the blade and you cannot see it.
A cat who suddenly stops keeping herself tidy, or who mats up when she never used to, is telling you something. Arthritis, being overweight, dental pain and simply getting older all stop a cat reaching parts of herself. That is a reason to mention it at the next appointment, not a grooming problem.
That last part is the one people have not heard. An indoor cat's back claws in particular can curl round far enough to grow into the pad, and it is painful long before it is obvious.
Most cats never need one. A bath is for a specific reason rather than a routine: something on the coat that should not be there and cannot be left for her to lick off, a skin condition your vet has given you a wash for, or an old or heavy cat who can no longer reach her own back end.
Whatever the reason, read the shampoo page first. The single most dangerous thing in a bathroom cupboard for a cat is a dog flea product.
What shampoo is safe for a dog or a cat