The shares in a non-UK company are not a UK situs asset. If the non-UK company is a private Jersey company it does not need to file accounts. Whilst there is a beneficial ownership register for companies in Jersey, this is private and not searchable by the public.
Contrast this with a UK company which would file accounts on public record, whose directors and shareholders would be listed on Companies House, a free searchable website, and whose shareholders would have a UK situs asset regardless of where in the world they live.
Additionally, family investment companies are becoming very popular in the UK, particularly amongst UK residents and domiciled individuals. This is largely due to the ability to roll up income and gains having paid only corporation tax (or if all income is dividends, then no tax).
Whilst the rules for non-UK companies might initially be considered more penal than UK companies in some circumstances, the rules are well understood and therefore can be planned for as appropriate.
Of course, if you do not have a UK tax position to worry about, a family investment company may simply be more familiar and better understood than a trust for your families' wealth planning and asset protection.