It certainly does NOT take three weeks to "clean up". That's not even close to the reality. If the FG is at, well, FG, it's done. It won't get "doner" by sitting.
I personally do NOT use clarifiers or things like gelatin, and I keg or bottle my beer at day 10-17, depending on what I"m making. I would challenge others to make a clearer, crisper, more finished beer.
Doing what you advise is great, if it works for you! However, it's not correct to give statements that 'you have to do this for XX weeks, don't take an SG reading because you'll oxidize the beer", etc.
Yeast will finish that "clean up" phase within about 24 hours of reaching FG. Then the beer will start to clear. That's an ideal time to package, when the beer is clear or clearing. That can be in 7 days, or 20 days. However, the beer is done fermenting when it has been at final gravity, as seen with a hydrometer, for at least 24 hours.
If it takes three weeks in a fermenter for the beer to be acceptable, there is a problem with process, technique, or ingredients. It can be packaged when it is ready, and it's usually within 14 days.