As far as I know, we already have proportional voting systems in the UK, in Scotland & Wales for the their Assemblies, in London for the GLA and for the Members of the European Parliament. I have experience of standing for and/or selecting/triggering Labour candidates in the latter positions.
While much focus of late has been on selecting/re-selecting MPs in the House of Commons these positions represent a special case.
Labour’s re-selection processes for “list” based seats in local government in England, currently only the GLA, unless we remain in the EU requires that incumbents are confirmed or otherwise as candidates (via a trigger ballot), and that new candidates are found and approved by panel. All the candidates are then ordered by a member’s vote, with the incumbents guaranteed the highest places.
This protection i.e. the guarantee that incumbents must get the highest ranking places on the list should be removed; the member’s votes should determine the order that incumbents and challengers are placed on the list, subject to the gender quota rules. The members should be offered an additional two candidates, who then become available for call up in the case that any of the selected candidates are unable to run.