It might feel less formulaic because it's more upfront. Following a formula without telling the other person about it can feel more robotic if you don't put your soul into it. Whereas you can still put in the right energy and effort into the OP's approach to make it work well. At the end of the day being human IMHO is what matters most.

> People smile when someone makes a bad pun also

Here too I think it's all about how the pun is delivered.