Mowing before seed = Future desert?

Still trying to figure out nature. I have an acre, I am happy with all the wild native grasses I get in the spring, except one that turns into "sticker balls" in the fall, getting all over our cats and causing us to throw out entire blankets unless we pick them out for hours.

FWIW it's oak/pine woodland, 50" rain, 1700', Sierra Nevada foothills, California.

If I mow before they (and all others) go to seed, say for 5 years, that would minimize their return right? But then I would lose my miners lettuce etc? And how would the good stuff pop up if I always mow before seed?

I feel like I would be creating a desert. My only solution is hand pulling the ID'd sticker weeds that the spit bugs call home as I pull the taproot out of the ground.

The idea of mowing only seems to benefit the ground with the leftover unbagged clippings, otherwise it seems kind of destructive from a bugs POV. So I would like to avoid that.

Any advice? I was thinking possibly mow for one season and hopefully 2 year old seed would pop up? Is that how seeds work? Thanks, I'm new here

I also live in grassland area in N CA. (lower down, further north, and other side of the valley). As far as I know, mowing or grazing is desirable (and mandated by law!) a certain distance out for fire control. The first 2-3 years I would try to minimize the times I had to do this, and would let the grass grow till the hot dry came on, and then scythe it once, gather this for mulch, compost, poultry bedding, etc. and then mow the stubble off short. Plenty of seed dropped. Now I'm envisioning adding a sheep or two to the system, so as to convert some of that grass into meat, and spare myself the sweaty hot work of scything and mowing in May or June. The sheep will be in the back, and I'm mowing already in the front and around the gardens, etc.; where the sheep won't be allowed anyway, and making these clippings into bag silage or hay for summer fodder.
In any case, on just an acre (I have 1 1/2), I would think more than plenty of seed would blow in from outside to keep your land growing stuff forever, unless you're surrounded by plowed fields. Also, you could deliberately tweak the mix by seeding or selectively mowing. I deliberately avoid patches of clover and wildflowers so as to encourage them, while focusing efforts against thistles, star-thistle, and such like...

Yeah, the 10 acre field across the street is all star thistle, but luckily I have none. Which makes me wonder how far seeds really blow. I have trouble trusting that method. I could buy ground cover seeds but I like the fact that the ones I have are true natives. And I bet I would miss a few to replace and completely lose that species.

I need some animals too. We border some type of uncared for BLM land with a tidal wave of poison oak crawling through my fence.

No defensible space on their side either. Makes me wonder if they are required to provide that?

Spot plant with protection to establish trees, shrubs, mow paths and leave areas wild, convert wild grass into animal produce, pigs sheep poultry, wild trapping. Develop planting, sowing and grazing rotation.