Handwriting instruction survives in a period when most adult writing is typed. The reasons are about what the act of forming letters does rather than about tradition.
Producing a letter supports recognising it
Writing a letter by hand requires producing its shape from memory, one stroke at a time, and every attempt is slightly different.
That variability appears to help rather than hinder. Encountering many versions of a letter, including one's own imperfect ones, supports recognising it across fonts and handwriting.
Selecting a key labelled with a letter is a matching task instead. It confirms recognition without requiring the shape to be generated, so the production element is absent.
Automaticity is the real goal
Composing a sentence involves holding an idea, choosing words, ordering them and monitoring what has already been written. All of that competes for limited working memory.
While letter formation still requires conscious effort, it consumes part of that capacity, and the writing produced is shorter and simpler than the child's spoken language.
Once handwriting becomes automatic, the capacity is released and written composition improves without any instruction in composition having taken place.
Legibility and speed are separate problems
A child can write neatly and slowly, or quickly and illegibly, and the two difficulties have different causes and different remedies.
Speed usually improves with practice and automaticity, while legibility often depends on grip, posture, letter formation habits and sometimes on underlying motor difficulties.
Schools generally assess these separately for that reason, and a report describing untidy writing is not necessarily describing the same problem as one describing slow writing.
Note-taking imposes a useful constraint
Writing by hand is slower than typing, so a person taking notes cannot record everything and must decide what matters and how to condense it.
That selection and rephrasing is itself processing. Typing fast enough to transcribe verbatim allows notes to be produced without the material being understood.
This is why the handwriting question resurfaces at secondary and university level, long after letter formation has stopped being an issue.
Where typing belongs
Keyboard skills are necessary and taught alongside handwriting in most systems, and for some students typing is the appropriate primary medium.
Children with significant motor difficulties, or with conditions affecting written production, may be assessed as needing a keyboard, and that decision is made by professionals working with the school.
For most children the two coexist, with handwriting carrying the early learning-to-write phase and typing taking over volume work later.