These Henbit are pretty! I have read the name before but have no personal experience.
I have become increasingly fascinated with the local weeds. Bit by bit I am learning about several of them. My latest fascination is with promoting native plants. Guess what. A lot of our weeds are invasive species, not a good food source for the native creatures so totally counter to the food web.
As for favs, I have a few. Dewberries(an eastern U.S. trailing vine cousin to blackberries) ...are a native weed here. I am actively promoting them in my back yard, and they are blooming right now. The birds will likely beat me to the berries unless I throw bird netting over them. Either way they'll feed somebody.

I have blue mist wild ageratum also vying for the same areas as the dewberries.

There is a little golden daisylike flower I have blooming in boggy areas of my yard in the fall. Haven't figured out which of the many similar looking species it is.

And finally, I have a lawn weed that a very low, ground-hugging vine that blooms adorable quarter inch white 4-petal star flowers in several cycles from spring to fall. I found a reference for it, though the name escapes me at the moment. I would be happy to replace all my remaining lawn with that. It requires no mowing, but it does die back to the ground with the first winter frost.. I have no photo of that, unfortunately.

Until they take over the garden, I don't mind invasive flowers. When they get in the garden is when the battle begins. A certain columbine has a tendency to spread its seeds everywhere and when established it's hard to remove without digging it out. The most invasive plant around here is goutweed. It's almost impossible to fully remove from a garden.

Dandelions!!!!!!!!! Harbingers of warmer weather!

Seems like a good addition to any garden.

Johnny Jump Up - they can have as much of my lawn as they like [gardenersnet.com]

Pretty plant. I grow weeds indoors in pots on my window sills.
Here's some Google info on this plant:
Edible
Henbit can be consumed fresh or cooked as an edible herb, and it can be used in teas. The stem, flowers, and leaves are edible, and although this is in the mint family, many people say it tastes slightly like raw kale, not like mint. Henbit is very nutritious, high in iron, vitamins and fibre. You can add raw henbit to salads, soups, wraps, or green smoothies. According to Natural Medicinal Herbs (dot net) this plant is anti-rheumatic, diaphoretic, an excitant, febrifuge, a laxative and a stimulant.

Similar Plants

Here in Australia but in fact also around the world the poisonous weed echium plantagineum known as Paterson's Curse or Salvation Jane is considered by some, Prince Charles amongst them, to be pretty :

[en.m.wikipedia.org]

Here are old friends Jason & Chloe Roweth singing about it:

Not familiar with that particular one . I do rather like both the clover and a plant my Mother called Wandering Jew , that I'm certain the HOA considers weeds .