Lots of things in D&D are left to DM fiat. Milestone leveling frees the DM up from tracking XP, and tracking XP is a deal-breaker for some DMs.
Can't see why, as it's trivially easy to do.
The trick is that during the session all you track is who got in on what (see below), which takes maybe 10-15 seconds per encounter, and then rather than stopping the session to work out the actual numbers do that sometime during the week.
How I do it during the session looks something like this: (all the dashes are just for spacing)
- - - - - - - - - - - - 4 Orcs - - sec door - - trap - - hydra 6hd - - [etc.]
Aloysius - - - - - - - XX - - - - - - - - - - - -XX - - - - XX - - - - -
Bjarnni - - - - - - - - XX - - - - - - XX - - - - - - - - - -XX - - - - -
Coriander - - - - - - 1/2 - - - - - -XX - - - -XX - - - - XX - - - - -
Dumystor - - - - - - - - - - - - - - - - - - - -(died)
Eohyl - - - - - - - - - XX - - - - - - - - - - - -1/2 - - - - XX - - - - -
Falstaffe - - - - - - - XX - - - - - - XX - - - - XX - - - - XX - - - - -
Pre-session I've listed the characters. During the session all I need to do is note what the encounter was with, and ticks for who got involved (or 1/2-notatoons for those with peripheral involvement, etc.), and this takes no time at all during play. During the week I'll go through, work out the numbers, divide them down, and write the results next to each tick. Here, each tick under the "4 Orcs" heading might have "23" written next to it, while the "1/2" would have "12".
Once I give out these xp - let's say I give them out at this point - I'd draw a big thick line down the page under where it says "[etc.]" to show me where the next batch begins.
Here, Falstaffe would ge the most as she got in on everything. Dumystor wouldn't get any, as his only contribution to anything was to die.
One of the advantages of milestone leveling is that it levels the playing field between players who are very social and proactive/aggressive and players who are less so.
Call me cruel, perhaps, but I see that as more of a bug than a feature; in that it rewards passive behavior rather than trying to change it.