Weed control can come in many forms. Some plants do better in more acidic soil vs basic, and native grasses tend to have a range of optimal pH different from broadleaf plants. As well, cutting strategy can help via shading--if the grasses are taller than the weeds, they get more light and grow taller still and choke out the weeds from getting sun.
Part of the problem with lawns in general is the ideal lawn, like the magazine lawn, tends to be a monoculture. But a really healthy, low-maintenance pasture tends to be a polyculture of many grasses, a few legumes (e.g., clover), and the occasional broadleaf (dandelions are great for instance when it comes to improving soil structure--their roots can really help aerate compacted soil).
Part of the problem with lawns in general is the ideal lawn, like the magazine lawn, tends to be a monoculture. But a really healthy, low-maintenance pasture tends to be a polyculture of many grasses, a few legumes (e.g., clover), and the occasional broadleaf (dandelions are great for instance when it comes to improving soil structure--their roots can really help aerate compacted soil).