Movements will always exist between the upper and the charging handle, they don't matter.
Now that's out of the way, we can explain how this happens.
Depth of the charging handle latch pocket on the upper:
Width, height, and location:
Of the few uppers we measured, below are their respective CH latch pocket depths:
Colt A2: 0.0610
Centurion Arms forged: 00745
Centurion Arms billet: 0.0725
No name. unmarked: 0.0875
Vltor MUR: 0.0555
CMT made FCD URF: 0.0645
The depth of the charging handle latch pocket on the upper can and does determine how much movement can manifest. The deeper the pocket, the looser the spring loaded CH latch is engaging it.
Colt A2 upper at 0.0610 depth:
Unnamed, unbranded upper at 0.875:
It is our opinion that the rattle is immaterial. Some parts in an AR require a very high degree of precision and have tight tolerances, this isn't one of them. Unless very tight tolerances are called for, the tighter the fit between two reciprocating parts, the less fault tolerance it has, it is not beneficial when a charging handle can't tolerate sand, dirt and debris that invariably find their way in.
In the case of the charging handle latch pocket, the width has a +0.00/- 0.10 tolerance, and the distance of the pocket can vary by -0.010, neither are very precise tolerances, but none are needed here.
Tighter is better isn't true for many areas in an AR15/M16. There are components in an AR15 that do have, and require rather tight tolerances, there are also parts that don't, and can't benefit from them. There is no correlation between a tight fitting upper and lower and accuracy, for instance. Efforts to produce a tight fit has led to some very questionable products and methods that are a waste of money and energy, as they don't help the users or the weapon systems in anyway, and often introduce undesirable and unintended consequences.
Back to the charging handle. Between a tight fitting charging handle with less movement and one that is in spec, but looser and makes more noise when shaken, there is zero functional difference. Some areas of the AR have loose tolerances for good reasons, we do not make things tighter for the appearance of quality that is but a false impression, going against TDP prints is no different than ignoring best practices recommended by manufacturers and designers.
If it is one's preference to have tight fitting parts even if they're specified to be loose, it's a preference. If it's a preference, there's no right or wrong, it's a choice and no justification is required. We do believe to draw a distinction between specifications / tolerances and preferences.