Why do UK Supreme Court Justices read aloud their judgments?
To add to Dale M's answer:
It's not just the Supreme Court that must read out judgements: all courts that pass sentence as required to do so. This is a legal requirement under s.52 of the Sentencing Act 2020 to ensure the defendant, victims and general public know what has been decided and why, and what the punishment is:
(1) A court passing sentence on an offender has the duties in subsections (2) and (3).
(2) The court must state in open court, in ordinary language and in general terms, the court's reasons for deciding on the sentence.
(3) The court must explain to the offender in ordinary language—
(a) the effect of the sentence,
(b) the effects of non-compliance with any order that the offender is required to comply with and that forms part of the sentence,
(c) any power of the court to vary or review any order that forms part of the sentence, and
(d) the effects of failure to pay a fine, if the sentence consists of or includes a fine.