Going late means you miss some of the stuff.
For what it's worth, when I asked my wife after my earlier post, she thought it shouldn't really matter and that I'm exaggerating the effect. According to her, most of the things that shut down are from people who come from the countryside to work and then go home for the holiday, so it's more like smaller businesses and stuff.
An example my wife gave is a girl she grew up with who employed a nanny from the countryside. When Tet came, the nanny went home to see her family and then just basically ghosted my wife's friend and never came back. Apparently, that sort of thing isn't uncommon as they either are too homesick to return or look for something better, but it results in a little slower pace for some things during the holiday.
According to my wife, people in the cities still have plenty of stuff to do and we were maybe just being a bit lazy hanging around with her family. So... I might actually be coming around to spending the holiday there instead. Either way though, it's great and you'll have a good time.