@Fernapple
I can't know for certain if Sweet Kate seeds, but the ordinary green one does. It made its way to our front yard in the river stone by the curb.
The ordinary green one dies after a while for us too. Big patches one year, dead the next. Sweet Kate is at least 10 years old. It needs full sun to have bright yellow foliage.

@RussRAB
The common variety has green foliage and will seed everywhere. Maybe Sweet Kate seeds everywhere and reverts back to green foliage. It's hard to tell. I find spiderwort growing in a few different places from seed in the garden.
Once established the spiderwort is hard to remove and will grow back with a tiny piece of root.

@flower_nut Your description is consistent with my experience although I haven't made an effort to remove the volunteers from my yard - they just get mowed short with the grass.

@RussRAB
The seeds seem to grow between the rocks I have around the gardens. If you pull them out they come back. The roots are thin and grow back with any pieces left in the ground. These are difficult to get rid of without a lot of work. I agree, mow all the suckers down.

@MojoDave
The overall consensus is in your favour when beauty is on your side.
The flower is winning. Thanks!

@Spinliesel
Thank you. I'd like to see the flower of a variegated spiderwort. Could you share a photo whenever possible?

@flower_nut I promise to take some pictures next year. Don't have any from this year, sorry.

@Spinliesel
Not to worry! I always look forward to a new season. This coming season I can share with all of you.

@HippieChick58
The foliage fades is beaten by the weather and the wind sweeps it against a rock. It looks its best in the first photo. The flowers open and close each day. It's a top ten perennial me.

@Heidi68
In the correct light, it makes a great photo.
Of course, I think all flower photos are great. I have thousands and if I repeat photos it's because I really like it.

@flower_nut you never see too many flowers or flower photos - imo.

@Heidi68 You're so right!