i think you may misunderstand how conditioning works and how the cleaning up phase works. the cleaning up phase is the 24-48 hr period as fermentation is coming to a completion and before the yeast start to consider going dormant, and they will consume some of the by-products that they produced in the first 24-48 hrs of fermentation.
conditioning isn't a result of yeast working. it's simply the flavors in the beer melding together. alcohol doesn't condition out. it's always present. it's just that all of the flavors haven't melded together yet. it's called green beer. green beer can be sent to a secondary for conditioning or it can be packaged for conditioning (or, obviously, if you choose to, you can condition in the primary). a lot of the bigger belgian breweries leave their beer in the primary for about a week. then transfer to secondary and cold condition or lager for another 2-3 weeks. then bring back up to room temps and bottle referment for 2-3 weeks. then ship.
either way, like i said, it's fine if you want to condition your bottles in primary instead of in bottles or kegs or secondaries. i'm not telling you to stop doing that. i'm simply saying that to tell someone that the beer must sit that long in primary in order to condition isn't exactly truthful info. it's just your method, and i'm sure you produce great beers with it. But that doesn't mean that other people aren't using other methods and still making great beer.
This.
There are cleanup functions that require contact with the yeast cake, such as reduction of acetaldehyde and diacetyl produced normally during fermentation as part of the compounds that eventually become ethanol. Once the sugars are fully consumed, the yeast then go and break down/reabsorb the compounds. But this happens rapidly after fermentation, usually 24-48 hours after FG is reached as said above. Now, if you dramatically underpitch, underoxygenate, and do not properly control your fermentation temp, then more intermediaries could be present, and more time may be needed to clean them up. This "leave everything in the fermenter for three to four weeks" is something that may be a good idea for new brewers, but it is not strictly necessary when your fermentation is on point (now, some beers will take longer to ferment, lagers take long, and some yeasts like Wyeast 3724 can be notoriously slow, and my Belgians in general seem to take the longest to reach FG, which if I understand my yeast biology is to be expected). I have beers that hit FG in 2-4 days (English session ales), and are fully conditioned by day 4-5, and if I were to keg and force carb, could go fully grain to glass in less than a week. I don't keg, but I've racked to a cask at 7 days, primed 5, and gone grain to glass in 12 days before. It's usually easiest for me to deal with things on weekends, I usually package at about 2 weeks. If I have time earlier, sometimes I'll do it earlier. If I don't have time, I'll let it sit longer. I've gone upwards to 5 weeks of primary with no ill effects assuming that the temp stays cool (hold at fermentation temp, raise 2-3 degrees after FG to facilitate reduction of acetaldehyde and diacetyl, and then cool down to cellar temp is what I try and do, if not fully cold crash/lager). I've left beers in primary for ~5 weeks in the upper 70s and unstable, and gotten minor off-flavors as a result (not autolysis, more soapy, probably from lipids/fatty acids in trub or something).
Point is, mellowing of alcohol need not happen in primary. That can happen in the bottle, or keg, or if you so desire, a secondary.
