The JLPT does not ask you to write anything. Every question at every level is multiple choice, answered by filling in a bubble. There is no composition, no dictation, and no handwriting.
The same is true of JFT-Basic: kanji requirements.
This has a practical consequence that divides opinion among learners.
What is actually tested
Recognition and reading. Given a kanji compound, can you choose its reading? Given a reading, can you choose the right kanji? Can you read a passage that contains kanji fluently enough to answer a question about it?
All three are recognition tasks. None requires you to produce a character from memory.
The case for not learning to write
Writing practice is slow. Producing a kanji from memory takes an order of magnitude more study time than recognising it, and for exam purposes it buys nothing.
If your deadline is a test in five months and your kanji count is short, time spent on stroke order is time not spent on the 300 words you still need. For exam efficiency alone, drop handwriting.
The case for learning some anyway
Three arguments, and they are not weak:
Writing teaches you to see. Kanji that differ by two strokes - 待 and 持, 未 and 末 - stay distinct in your mind once you have written them. Recognition-only learners confuse similar characters more often, which is exactly how exam distractors are built: kanji look-alikes.
Life in Japan involves forms. Address, name, date, workplace forms, bank forms. You can manage with kana and a phone, but it is friction.
Components stick better. Writing makes radicals memorable, and radicals are what let you guess at unknown kanji later.
A middle path
What we suggest to most students:
- Write each new kanji five times when you first meet it, then never again. Enough to fix the shape and the components; not enough to eat your study time.
- Drill recognition daily, with spaced repetition, in both directions - kanji to reading and reading to kanji. Spaced repetition.
- Write by hand only the characters you will actually need to produce: your name and address in katakana, numbers, days of the week.
Learn kanji inside words
The single most important point, whichever side of the argument you take. 生 has many readings and they are not learnable in isolation; 学生, 先生 and 生まれる are learnable.
Learn the word, get the kanji free. Kanji for beginners and kanji by level.
And if handwriting is your bottleneck rather than your hobby, note that nothing in either exam will ever ask for it.