There are valid concerns and invalid concerns because a huge assumption is that the DM won't use the rules about being able to address edge cases. A large and complex system will always end up with some weird combination that can be abused, but as long as there are a reasonable number and they don't come up often then the system is fine.

5e does have some basic problems like exhaustion undercutting barbarian rages, but the vast majority of online examples of things being broken involve a massive misreading of the rules by ignoring context, vague rules (a separate problem from being broken), or people thinking an outcome is broken when it is just the system working as intended. Like being able to use Shield Master to knock down/shove opponents with a bonus action before making attacks since the bonus action rules say it can be in any order. Knock them off a cliff and no opponents? Ok, since you must attack on the same turn your action is lost because it could only being used to attack. That doesn't make it broken, and it is addressed as an edge case by the DM.

Again, some things are broken, but most of the things people call broken are just edge cases that can easily be handled by the DM being overblown in a game that has too much focus on fiddly combat while being written with the story first.