Are burr clovers a big deal?

Our "lawn" is full of weeds and we love it. Clovers, pennyroyal, chives, flowers - and a bunch of other things we haven't figured out yet.

I know clovers are good for soil, so when I saw these clovers growing out back by my trees I was excited. Then I realized they were rather long - let's say, "eating" into my kill mulch zone by nearly a foot! and had prickly balls all over them. I started to think these weren't the "good" kind of clovers.

As of right now I've just kind of been scooting them off my kill mulch zone.

Do I need to do anything about these, or just let them be? I know I have invasive weeds (hello, pennyroyal!), but I'm not really wanting to have an all out battle unless it's something that will hurt us/our trees. I really don't want to spray.

Advice? Thanks!

This is a plant that I hate!
I don't hate many plants.  The other one would be sand spurs.

I know it has the same benefits that other clover have.  I generally feel that most plants have some benefits.

Even a very tiny burr clover will produce hundreds of burrs.  If you don't mind them sticking to everything including your dog if you have one then let them grow.  I feel sorry for your neighbors.

The only way I know to get rid of them in your lawn is by pulling them up.  We never had them until this year (at this place) and I have already pulled up 4 or 5 grocery bags full.

If you have large areas of burr clover or don't mind killing some grass, you can use the propane torch/flame thrower.

There are few things I go out of my way to remove, but they tend to be plants that make my garden less enjoyable for what ever reason.

I know that some people love thistles, stinging nettles, and various thorny plants, but for me they are simply not welcome. There are other, more sociable, plants that could fill those gaps. Ones that don't stop me gardening barefoot!