I'm not sure why, but the very few places in my yard where the soil is good enough for grass to grow, have very few weeds except for dandilions and blackberries, which are pretty easy to keep uprooting before they go to seed.
On the crummy parts of my yard, even weeds have a hard time, but there are some, and if my beds were near them, this mowing tip would be an excellent idea.
However, where I have amended the soil in raised beds ... there are such a quantity and variety of thriving weeds that they are a major source of feed for my compost heap!
If I cared about the grass, I would worry about weeds spreading from the beds into the lawn.