For a dramatic example, consider the VESA framebuffer console, a slow serial link, or a bad SSH connection with a good CPU on the other end.
With enough terminal output it will bottleneck whatever you're doing. Sometimes extremely dramatically so. To the point of adding hours to a task in really bad cases.
For such situations, it often helps a lot to run remote tasks in something like screen and only switch to it to check progress once in a while.
At the very laziest &> foo your output. Or preferably add logging to your application. Go back 20 years and you wouldn't have had the luxury of spewing hundreds of megabytes of text to a remote terminal for no reason.
Simple as that.
However because how Linux graphics system was developed, there is a lot of extra latency and bad software out there, so it might be noticeable.