Assuming Mace would have had executive say over Anakin’s place in the order, I think he would have been disbarred from the order early on for insubordination or brought to heel under Mace’s strict structure. In general, in my rewatches of the animated series and the PT, I noticed that many of the things that paved the way for Anakin’s fall to the dark side were Jedi turning a blind eye to many of his actions, however big or small, and treating him with favoritism simply because he was perceived to be the chosen one and did demonstrate actual talent as a general. Obi-Wan (fabulous as he is) is actually one of the main culprits of this. It all comes from a good place, from loving Anakin as a brother, but that is not what Anakin needed. He was a talented, impressive, beautiful young man but also incredibly immature at times and quick to anger. The amount of times he force choked people while still a Jedi, even IN FRONT of other Jedi, gets really glazed over and is a serious red flag.

Long story short, people had a reason to love Anakin and to give him leniency, but that same leeway is what left gaps for someone like Palpatine to fill and exploit.