I tried to think of what would be the opposite of ‘Move fast and break things’. Zuckerberg’s often quoted ideal is interpreted (or misinterpreted) a thousand different ways. I like the simplest interpretation – challenge things, try a lot of stuff and fail fast (so you get to the ‘right’ solution faster).

“Move Slow and Follow Rules” probably isn’t a good thing to automatically put in play – seems like almost a default setting we often see on most productions.
Move slow and you get less done. Sure there are times you need to move slow. You need to probably move slow if you are learning. You might also need to move slow(er) if accuracy or quality is not at spec. If neither of those are at play, you should consider moving faster (generally speaking, people could embrace a little more urgency on most shows).
Carefully follow your established rules and you will likely get the same results. Sometimes, you want the exact same results (assuming things are going well and high quality), but most times we want better results and linked improvement. You get that from small iterations, adaptations to the rules. You want exponential results? You better be ok with breaking some things.
‘Move slow and follow the rules’ is a good thing to tell the novice, someone inexperienced, or someone struggling with quality. Otherwise, I’m always going to recommend we take a good look at things, move faster and adapt.