Well true but you don't have to accept all the people who reach the final threshold until you've actually raised it all that way, so it allows you to reject more people while avoiding nasty near misses. It also allows you to defer the final decision indefinitely, taking into account only those near misses that actually occur.

For example I reckon you could get it to converge by e.g. accepting anyone who comes closer to the threshold than anyone before, this could avoid all near misses (for some definition of 'near miss') while almost certainly remaining bounded (unproven, ask your local mathematician for advice).