The tellraw and say commands don't have a success output. While the results given by those commands are already their own success message, there's not anything to clear a command block's previous output when the command is ran in one. This means that they will keep displaying the same output they had prior to the command execution, with the same timestamp and result, and without keeping track of the current command.

Steps to Reproduce:
1- Insert any command other than say or tellraw in a command block.
2- Power it and check the output.
3- Insert a say or tellraw command.
4- Power it again. Instead of clearing/updating the output (since there was not any), the command block will still display the previous one, with no updates to timestamp and result.

With other printing commands, such as tell/msg/w, this doesn't happen. That's because the command block acts as a player in those commands, in a way that the target player will receive @ whispered to you, and the command block will display You whispered to [player].