Upvote:2
As noted on the Wiki page, grass seed was imported to the new world to improve pasturage for livestock. A kept lawn is, in its conception, a decorative pasture - a marker of status. So the best grass for pasture was the best grass for commons and household yards where a sheep or goat could graze... which became the standard for purely decorative lawns. As stated in the wiki article, Kentucky Blue Grass and Bermuda Grass are the most productive pasturage in their respective climates - and it's worth noting they're the most prized for lawns and landscaping in those same regions as well.
Upvote:4
"The grass family is one of the most widely distributed and abundant groups of plants on Earth. Grasses are found on every continent, and are absent only from central Greenland and much of Antarctica" Wikipedia page It seems unlikely that grass seed would ever have been really all the prized given it's natural abundance basically everywhere. Grass also includes all grains (wheat etc, even rice), which should show it's ubiquity.
You do get grass species far away from their natural habitat (invasive species, those imported to reclaim wetland for do some specific land management role, those in peoples gardens etc) but that's probably a result of hugely expanded trade in the last couple of centuries. I believe it was in the 19th century when people started acquiring exotic ornamental plants in any serious fashion.
The only documented historical movement of grass I can find is the expansion of grain types cultivated in the fertile crescent across Eurasia, but that wasn't aesthetic at all. Movement of the harvest from grass was common though, and rice was newly available and pretty highly prized in medieval Europe... but not aesthetic again.