There are similar measures for bridge. OKBridge uses a Lehman rating for each player. Assuming the ACBL collects data from tournaments, it could give a chess-like rating to each player. Or, avoiding all complexity, it could simply report average percentage and average Victory Points for the last year in Regional play.
A proper measure will take into account your partner's rating. But it almost certainly will not take into account the fact that you play better with a familiar partner than an unfamiliar partner. So if you care about your rating, you will tend to play only with familiar partners, which I think is not good for sake of bridge.
There would also be ways of beating the system. A pro could sometimes play with another pro, they could do poorly on purpose, and their ratings would drop. (This would presumably be unethical.) Then when they played with a client, the rating system would see the pro as an ordinary player.
I mention the problems with accuracy just to point out that such measures are not trouble free. But I judge these problems to be minimal. The real problems I think are with enjoyment.
The distinctive features of masterpoints, as opposed to a rating system, is this. In the masterpoint system, when you play, you either go up or stay the same. In the chess-like rating system, you can also go down. Psychologically, this means that in the masterpoint system, you can't "lose". Because of this, the masterpoint system is going to be more enjoyable than the chess-system.
Put experientially, you go to the club and do poorly. You are frustrated. But you can blow it off -- you hoped to win something, you didn't, but it doesn't matter for masterpoints whether you were middle or bottom. And you would have been no better off to stay home. If you are also lowering your rating, that is just one more frustration.
The ACBL collects money when you play; they don't collect any money when you stay home. Same for club owners and people running tournaments. So the ACBL, as a practical matter, is not going to eliminate masterpoints. And if they were smart, they would probably not construct a chess-like measure of ability, on the reasonable chance that that would decrease interest in masterpoints.
Or, we know that Donald Jones won more masterpoints last year than any other Life Master in Unit 112. Way to go Donald! If we had to guess who was the best player in Unit 112, of the players who started the year as Life Master, our best guess would be Donald.
If there was a chess-like rating, that rating would be a far more accurate. Therefore, we could do a much better job of guessing who was the best Life Master in Unit 112. But that would make Donald's win less valuable. If he has the highest rating, he didn't have to win more masterpoints than the other Life Masters to show he was better; if he doesn't have the highest rating, his win just shows that he played more often.
IMO, masterpoints increase member participation, bringing in more money to the ACBL. So I think the ACBL has an incentive not to develop an accurate chess-like measure of ability. Of course, other good reasons for having such a measure might outweigh this concern. And ultimately the administraters should be doing what is best for bridge and members of the ACBL. However, I think masterpoints are probably more enjoyable than a chess-like rating, so the best policy for members might also be not to have a chess-like rating.