The effect of removing this flag is very interesting—the value of the string stored in the variable is not deleted, but is "considered" incorrect and is not copied to new variables :)

perl -MDevel::Peek -e'$x = 3; qq($x); $x+=1; Dump $x; $y=$x; Dump $y'
SV = PVIV(0x15d75f4) at 0x15d57e4
  REFCNT = 1
  FLAGS = (IOK,pIOK)
  IV = 4
  PV = 0x1a53acc "3"\0
  CUR = 1
  LEN = 2
SV = PVIV(0x15d7604) at 0x15d64d4
  REFCNT = 1
  FLAGS = (IOK,pIOK)
  IV = 4
  PV = 0
[download]

You see—the PV (value of the string) for $x was not updated by the numeric operation and was not copied to $y. So, being strict, the variables after numification become not pure IV, but PVIV storing only integer, looking much like simple IV, which causes much less work to copy :)