Speed - absolutely use of a laptop provides an advantage. Typing is much quicker than writing by hand, especially for today’s students who on the whole type up term time work and take lecture notes on a laptop and rarely write essays at speed by hand.
Diagrams are difficult to produce on a laptop so are completed by hand on paper and included in the final submission where the exam is completed under special conditions.
There is no access to the internet in an exam which is typed, except in an online open book exam, where all candidates will be able to type.
A type-written script amongst handwritten scripts is a giveaway that a candidate has had special conditions for the exam, but the examiner won’t be aware of any additional writing time or rest breaks which may have been awarded, or whether the candidate has been in a smaller, quieter room on their own.
The advantage of using a laptop over writing by hand you hadn’t mentioned is the candidate’s ability to structure their essays more freely and to organise and reorganise their thoughts by cutting and pasting their script throughout the exam.
But absolutely, speed of typing over writing by hand is a main advantage.