Where do I start?

• I'm a gardener and so are the majority of people I spend time around. If you are mowing 3+ times a week and regularly spending money on fertilizer, soil tests, herbicides, fungicides, and insecticides, you have chosen the most expensive, time consuming thing you could possibly do with your yard. Unless you are a farmer as your livelihood, NOTHING else you could grow is that high maintenance. Nothing.
• Most turfgrasses are invasive species. I said it.
• The practice of "nuking" your lawn (killing everything in it and "starting over")...If you have a so-called "weed problem" this is probably the worst thing you can do.
• Listen to me very carefully: "Weed" seeds are everywhere. There is, at all times, a supply of seeds lying dormant in the soil, waiting for the right conditions to sprout. (It's called the "soil seed bank" and you can look it up.) They are capable of "waiting" for years, even decades. Furthermore, most "weed" species spread by wind, meaning you can't physically eliminate them from an outdoor area unless you...surround your entire yard with an incredibly fine mesh netting and never leave, I guess.
• Heavy management will make your "weed" problem progressively worse and worse because those plants are specifically adapted to colonize barren areas that recently underwent disastrous events that killed off most life.
• Basically all plants are adapted to live in the company of other organisms, and suffer when there are no other plants around. "Weeds" with deep taproots penetrate into and aerate the soil. Clover puts nitrogen in the ground that other plants need. Low ground covers keep the soil moist and stop the sun from baking your grass to a crisp.
• The plant "taking over" your lawn is probably not killing your grass. Your grass is dying and it's being replaced by something more suited to the environment. This is supposed to happen.
• Monocultures are notoriously susceptible to disease and mass die-offs. "Oh no a big patch of my lawn is dying!" Yeah, that happens when you plant monocultures. You set yourself up for this.
• "Why is there a bare patch in my yard/why won't grass grow well here?" Because in nature, each plant has a relatively narrow range of conditions it likes to grow in, so other plants it might otherwise compete with can stick to their preferred conditions and nobody has to compete directly. Win-win. Not all parts of your yard have the exact same amount of sun, moisture, etc. Expecting the plant life to look the same is unrealistic.
• Let me make this very clear: It is fully impossible to "solve" the problem of plants popping up in your yard that aren't your one favored variety of grass. You will be buying herbicides for the rest of your life, and it will get worse, not better, because willy-nilly use of herbicides is leading to plants developing herbicide resistance faster than we can come up with new herbicides.