Not directly answering the question, just some background info- Tall buttercup, Ranunculus acris, is one of (to me) the most bothersome invasive weeds (in nature, I define weeds primarily as non-native plants which are taking habitat away from
native plants; to farmers, it means plants not part of a crop nor edible to livestock- buttercup fits all of those definitions)- it is not much a plant of gardens of fields but rather mostly a plant of pastures which have not (recently at least) been plowed, and have mainly native plants used for livestock forage, often growing with common agricultural escape forage plants. The buttercup spreads here especially in damp/wet pastures that have been heavily grazed, though it will then spread into neighbouring wooded areas also, to a lesser degree.
I can't see mowing helping, since it spreads in overgrazed (not dry though) areas. There are usually still native plants among the buttercups, but obviously fewer.. it may not be replacing the smaller forbs such as marsh violets, but quite certainly is replacing grasses, sedges, rushes etc..
I don't know if mulching would work- probably if it were thick enough- I have doubts above cover crops, unless they were very tall, taller than the buttercup. When they pop up on my acreage occasionally, I dig them out. but don't know what you'd do in a field (obviously farmers here spray if they get around to it) unless you could find an animal that will eat them- cows certainly don't. Maybe the method of penning in horses- fed with hay- to trample them would work!
I forgot to add - regarding the idea of 'weeds' obviously common garden weeds that are really neglected food plants of old are a totally different issue, both because of their value as food, and also because they are generally not present in natural areas, at least not intact ones.. Nor do I have a huge concern about garden escapes that only introduce a few plants here and there into semi/natural plant communities, as that does not reduce biodiversity (hard to know, though, when those gentle invaders can become serious invaders that reduce biodiversity).. Native plants which seed themselves into garden beds and lawns are not weeds to me, even though sometimes they need to be thinned/removed/relocated. In my case, no intervention would mean I lived in a spruce forest before long..