He has no statue because he's not a Stark anymore. He's 3ER.
This is my take as well. Once you’re the 3ER, with all of time constantly populating your mind, the short timeframe of Brandon Stark is irrelevant. He no longer has any concept of nor loyalty to being a Stark. Brandon Stark is effectively dead. We have now the 3ER.
He has not statue because he is still alive in the time period which the other Starks have been shown to have died.
He’s still Brandon Stark to the people who would be around to make the statue. It’s not like they don’t view him as a Stark any longer.
Jon's not a stark either
I don’t know why, but I read ‘3ER’ as the ‘third eyer’
3ER? What does that stand for?
Wights
marching