Dump stats are extremely common. Role-playing flaws is actually quite fun.
However the mechanical limitations are that the most common dump stats by far are CHA, INT, and STR. 5e does introduce saving throws for these abilities but they are kind of stretch to rationalize and uncommon. Most importantly though, these stats really all suffer from being able to dump the stat, and letting someone else take care of the problem. If I have 12 INT, but my part's wizard has 18 INT, I might never see a return on my ability score investment.
BG3 does improve on this a little bit. STR is generally pretty useful on everyone for the carry weight and jump distance. A lot of INT checks are rolled when exploring so each party member contributes for more chances to succeed. But it is a puzzle that no tRPG has really solved to enable complete build freedom.
