What if it's an icon with a simple shape? How does that compare to noising up the table with long phrases and repetitive words? Is the cognitive tax if icons a lot higher or just a little higher? What if it's an app where the user will be using it for hours, so they'll quickly learn what the icons mean and will appreciate the space they save?
Is a tick icon really that big a deal in place of "Task completed"? Or a pencil instead of "Edit"? Sometimes you don't have a choice because of lack of space too. There's always tradeoffs to make. Obviously try to avoid icons that are hard to guess though but sometimes that's not always possible.
I can't say I've ever felt tired looking at icons in a table, but when designing I have had the experience of replacing wordy repetitive text with some intuitive icons in a complex table and it suddenly looking less intimidating.