I think it might be more valuable to ask about the advantages of a rating system.
Chess ratings are used to match players of similar skill into groups so that competition is between players of similar skill making the game more enjoyable - who wants to play in competition where you always lose - or always win?
It would be like being stranded on a desert island with only Wordle for entertainment.
Aggregation of players into skill 'bands' tends to prevent cheating since a cheat will rapidly end up outside their skill level.
Applying the same principles to Bridge a rating system would allow players to form pairings of appropriately similar skill level (temperament, system and language notwithstanding).
In this way a rating system will have two positive effects.
First, it will make it easier for players to form pairs at their appropriate skill level.
Second, it will make cheating much easier to detect in the event that a pair suddenly develops a remarkable cough-associated improvement (for example).
One consequence might be that tournaments could be organised into multiple 'leagues' in the same way that football is organised in the UK (except that Sheffield Wednesday really ought to be in the Premier League - most unfair).
Pairs would rise and fall over defined time periods from the bottom league to the Premier league.
The current method of assessing skill on the basis of green- or dung- coloured matchpoints (or even masterpoints) leaves a lot to be desired.
Green might be desirable to Lord Percy but is it really all that helpful in assessing skill?