While there is a legitimate argument to be made that having clubs fielding two teams in the competition hurts the competitive integrity of the tournament, one could also argue that it flies in the face of everything that makes the US Open Cup so great.
Personally, I have a love hate relationship with this tournament. On the one hand, I love watching lower league teams put it all on the line against higher division opponents. That's what makes the US Open Cup so much fun. On the other hand, I find watching MLS teams marching out B-squads or A-squads who aren't giving it their all, a major chore.
To me, what's most harmful to the competitive integrity of the US Open Cup isn't that teams like LA Galaxy II are able to compete in the same competition as their parent club, but rather that most MLS clubs don't truly compete in the tournament, which is why a team like the Philadelphia Union has been able to make the finals two years in a row, but not the playoffs.
And this is not the fault of MLS teams. It's just a reality that, from an upper division standpoint, the US Open Cup simply does not have the weight of a Supporters Shield, MLS Cup or CCL title, and those that would tell you otherwise are either insane or from Seattle.
And this is the true tragedy of the recent US Soccer ruling. While it makes sense from a competitive standpoint, it shuts out 8 teams who are far more likely to give their all in this tournament than the 8 teams they are owned by.