This weed’s root system underlies my entire front yard

I’ve been hand weeding pretty frequently and when I pull these up I end up with huge bald spots. Is this even a weed? I feel like I’m just tearing out the whole lawn at this point. Any tips on how to get rid of it? I’ve tried weed and feed plus pulling them out with hand tools. In zone 8b if that matters. Pictures of the bald spots in comments. Thank you in advance.