He can't. He is too slow.
Brogdon is a solid but unexceptional defender. He defends the SG position the best but can also defend the SF. He is at his worst man-to-man at PG but is a plus team defender there.
Smart is a truly great team defender and a solid man-to-man defender at PG. No comparison.
Solid but unexceptional? Man, you’re just pulling that out of your ass.
He’s an excellent defender and has an ACC DPOY under Tony Bennett to prove it.
He’s also done it on the pro level. That’s nonsense.
The NBA is a bigger faster more athletic league than the NCAA. Just because you were a top defender in the NCAA does not mean you will be one in the NBA.
When Brogdon was in Milwaukee, it was noted he lacked the quickness to cover top athletes at the SG position he was playing. As a 3&D player in MIL, Brogdon was considered an elite offensive player (50-40-90 guy with 4apg along with 15ppg) but only a solid defender rather than an elite one. There were always questions whether he should be considered an elite or even true 3&D guy (like Raja Bell) because Brogdon's defense wasn't good enough (or whether he was just a very good offensive player with solid D).
When Brogdon went to Indiana, he shifted down a position and his so-so quickness at SG became even more exposed on defense against quicker ball-handling guards that he met at PG. His size and switchability allowed him to be a positive as a a team defender as a big PG but he struggled in his one-on-one assignments at his position.
Brogdon is a useful defender but he is not Smart. Nor is he D White. Both of who are high level / exceptional defensive players.
Edit: Remember that guy BOS drafted 10 years ago named JaJuan Johnson (JJJ). He was a defensive player in the college but he was awful in the NBA. He didn't have enough muscle for the NBA game. NBA is bigger, faster, stronger, more athletic. Just because you were a great defender in college does not mean you will be a great defender in the NBA.
Brogdon as a big defensive PG needs quick mobile bigs behind him to help cover his lack of speed. The good news is we have that in BOS. We have Horford and Rob Williams and Grant Williams. Lots of mobile big men defenders to cover Brogdon's weakness defensively and to allow Brogdon's strengths (size, switchability) to add to our team D. That is the good news. We should be happy with that.