Onion Lawn!

OK, not ALL onion, but seriously,  if I want  aliums everywhere, what varieties should I choose?
I want them to self seed aggressively and spread throughout my landscape.
I'm open to using sets or seed or whatever else might work.
Bulbing, non-bulbing, bunching,  walking, ornamental, as long as they are edible and "invasive " I'm interested.

I have a couple fruitr trees with chives and garlic chives under it. they have kinda taken over (self-seeding) and they look like grasses in an orchard. Sadly I don't think that anything in the onion family could handle foot traffic. But your best bed will be chives/garlic-chives

Do you have nativew wild garlic(Allium canadense) growing in the area? It produces both bulblets and seeds and propagates from both easily. Not to be confused with wild onion or onion grass, which is considered a noxious weed.
Here is the page of Illinois wildflowers website.
https://www.illinoiswildflowers.info/prairie/plantx/wild_garlicx.htm

Egyptian walking onions would be a good choice, but I agree with the above post and think defined paths would probably be necessary to direct foot traffic. I don't think pickup football would be an option on an allium lawn.

There's an abandoned homestead around here where I get all kinds of stuff. There's garlic there that drops bulbils and reseeds itself in the field. The patch is slowly expanding.

Thanks for all the replies!
Right now the only "lawn" I have consists of smart weed.
I tried establishing a clover and orchard grass lawn, but the smart weed overwhelmed it.
I started thinking about an onion lawn while weed wacking mint at my second grow site.
The overwhelming scent almost brought tears to my eyes...

While I doubt any aliums could out compete smartweed, I would like to have  aliums growing in my containers, around my berry bushes and trees and in every corner if every bed.
Onions and garlic are probably the only vegetables eaten by every family member.
They also seem to be in every guild list.
I put onion tops into all my containers,  and have been rewarded with greens and flowers.
So, an onion lawn is silly but the idea of aliums that are as common as grass is what I'm about.

In addition to buying and spreading around the varieties yall mention,  I think I will plant a mixed bed of every kind of alium near our back door, and let them go to seed and  fight for dominance.

It's dormant during the summer here, but for a winter crop we have great results with Canadian onions.  They're a little stronger in flavor than the green onions sold at the store but the are interchangeable in all uses we've tried.  When the weather warms up the form flower heads that are half bulbil and half flower.  After going to seed they dry up and go dormant till next winter. I pull the larger ones escaping to the lawn before the first mow and they have small pearl onion bulbs.  The only work I put in is harvesting and washing and they cover a bigger portion of their bed every year.  

I suspect they would intercrop very well with warm season plants that will just begin sprouting or breaking dormancy as the onions die down.  As I write this I am realizing that I should try planting sweet potatoes in that bed.  They are nearly perennial here and I bet the onions would slow down the insect predation on the roots.  The onions would still be dormant at harvest time so I could still dig up the roots.

For aggressive self-seeding, you can’t beat garlic chives (allium tuberosum).  Bees LOVE the flowers also.

It will form dense clumps 12-18 inches tall.

When I lived in the mid Atlantic, there was something everyone called “onion grass” that was a small, mowable chive-like plant that the leaves were really the size of grass blades.  I don’t know that it is a thing for sale anywhere, it just showed up on its own in lawns. If you google “onion grass” you’ll get lots of “lawn care” pros telling you how to get rid of it.

In NZ, our local "onion weed" seems to be different to the common one in the US. If you can find Nothoscordum × borbonicum, it's got lovely oniony/garlicy leaves and small tubers you can use as pickling onions. I've seen it take over whole verges with its oniony goodness. A great plant for some foraging, for sure. Requires zero care and survives moderate drought. Other names for this plant include honeybells and fragrant false garlic. It's actually quite pretty in my opinion with lovely bell-shaped white flowers.