It’s still around but it is called Frazee. Spelling is sounded out as fraza.
On Google I found a large carpet dealer named Frazee, and an allusion to it as a type of carpet, but not any page advertising that kind of carpet under that name.
Shag was doubtless intended to be fun. It would be a grand hassle to shampoo and vacuum compared to more conservative carpets.
Speaking of vacuuming, the home vacuum cleaner didn’t come into vogue until the early 1900s. Before that, you had to have a truck mounted unit come similar to the ones that do furnace duct cleaning today. They could make quite a racket as they were gasoline engine powered. With the home vacuum cleaner, carpet was viewed as more practical in homes.