I always rebook for a better rate, whatever it is.
For points bookings unless it's a 5nt stay I book one night at a time. For cash rates I sometimes break it up, but always look at different rates for different segments of a stay. I can often save hundreds per stay by using two different rate codes.
Hotels often comment on it and I just respond with some many rates and variable pts they create the game, I just play it.
The only downside is ENCs and pts often get messed up. I've had a few really frustrating IT mistakes that lead to hijacked FNAs, points or incorrect rates. Any regular Marriott guest should know to take lots of screenshots and save all emails.