Routing around the arc is the equivalent to going round the race track hold. You are absolutely correct, the pilots will only have a theoretical maximum distance. However, once cleared to route direct to the merge point, the fms updates the rest of the distance to touchdown.
Pilots are cleared to the merge point as soon as the one ahead is established inbound to the merge point and is the appropriate distance ahead.
It works. When I first heard about it I wasn't convinced either, but I'm slowly coming around to the idea. 😀