Many years ago Milwaukee was plagued with chuck issues. The one your dealing with doesn't look much different than one I had that was complete garbage. I ended up replacing it with a Metabo Futuro Plus chuck. At the time it was cheaper than other well known brands.
Here's an old picture:
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There are two main German chuck manufacturers.
Rohm/Roehm, and Metabo, (and Albrecht, but Albrecht doesn’t make chucks meant for portable drills, just ultra precise machinist chucks).
Both manufacturers offer a few different qualities of keyless chuck for “portable drills”.
The all steel “lightweight” chucks are the Futuro Plus, from Metabo, and the Rohm Extra, from Rohm.
Both chuck types are available in various thread mounts, and both are available in single sleeve and double sleeve versions.
Double sleeve chicks are needed for drills without spindle locks, whereas single sleeve chucks are specifically intended for drills with spindle locks, usually cordless drills, although corded drills with spindle locks exist, and earlier cordless drills routinely didn’t have spindle locks.
The Rohm Extra, and Metabo Futuro Plus chucks are similar enough that both are likely manufactured by one or the other manufacturer, although I’m not sure which one.
The same chucks are also sold rebranded by Bosch, and KWB, and likely other power tool accessory suppliers.
There is also a version of the chucks with an outer sleeve molded from plastic, (both single and double sleeve versions).
A version of which is used by Festool.
I truly hate the plastic versions of these chucks, and don’t know why they exist, other than weight savings, or power tool companies trying to shave pennies off cost.
Technically, the plastic versions might be less likely to damage materials if the rub against them while a drill is running, but I find that sort of an excuse.
The Festool versions of the chucks in my opinion ****.
I don’t know the full history of the technicals of the chucks, but I know the similar, but nit identical Yukiwa keyless chucks from Japan, originally did not have the ratcheting feature found on most current chucks, and would not lock as well.
Yukiwa later added the ratcheting feature into their all steel cordless chucks, but the newer ratcheting versions look almost identical to the older non—ratcheting chucks.
Depending on where tools are being purchased, the various tool manufacturers will usually supply different chucks on the same tool models.
Milwaukee drills sold in Europe used to usually get the Rohm Extra style chucks.
The same drills sold in the USA, where usually supplied with Japanese Yukiwa chucks.
Drills sold in France may be supplied with chucks made in France by LFA.
Dewalt has offered drills in the USA using chucks from Rohm, LFA, Yukiwa (I think), and Jacobs, and maybe others.
As far as Yukiwa goes, the drill chucks they manufactured from the 1990s thru the early 2000s, that were used on Milwaukee drills where excellent from what I recall, and at least to me seemed better than the Rohm Metabo all steel keyless chucks.
Fein uses Rohm chucks, but other than some of the crappy plastic sleeved versions used on cordless drills, Fein mostly uses Rohm chucks from the Supra SK series, which are fully “billet” machined chucks, closer to the Rohm machinist chucks made for stationary equipment, just with slightly lighter dimensions.
Hilti uses Rohm Supra SK or Metabo Futuro Top keyless chuck for rotary hammer keyless drill bit adapters, but something similar to the Rohm Extra for some cordless drills, and some sort of plastic chick on other cordless drills.
