What is a good age to introduce children to a martial art?

For myself, the main criteria is not to do damage to the child's growth.

Repeated strains on joints (wrist locks for example) and repeated impacts can have negative effectsmuch later in life. Some aikido dojo will have a syllabus for under 18s, other will just refuse to train anyone under the age of 18. What adults do is not necessarily what a child should do. Having a junior syllabus is a good indication that someone has thought about that.

Psychologically, some children are much more mature than others at the same age. But all do need good teachers to get discipline and a healthy states of mind in which to approach martial arts -- including western ones like fencing. Competition should be about learning to grow and not crushing your enemies and hearing the lamentation of their women.

In my not so humble opinion, the right criteria is "What will lead to the best development of the child, both mentally and physically, without causing harm?". The answer to that, will vary between child, parents, teachers and the law of your country.

Some McDojos will be teaching badly and those should be avoided at all costs.