Rich and Sharon are known to use the phrase Let's Do That, or Yeah, let's do that or maybe let's do so, but they really don't have a choice. My mother worked in television for a long time and she knows that TWC uses something called a TelePrompTer or what some people call an Autocue. (more info
here) The TelePrompTer tells Rich and Sharon what to say. Let's Do That is not their catchphrase, it's in the script and it is what the TelePrompTer shows. Therefore, Let's Do That is not really something that they say if they want. It is mandatory. You can still make fun of them for saying it but this is the truth.