That said, I think the usual objection to the space mirror approach is that you can get the same result much cheaper by spreading a cloud of tiny reflective particles into the upper atmosphere. (I've heard of proposals that would just mandate some additive to the fuel used by large passenger aircraft.)
Making the sky 1% hazier is kind of uninspiring (especially when compared to giant orbital mirrors, which could also act as death-rays if aligned and focused properly), but if it's cheap and is likely to work, then maybe it's worth a try.
(Unfortunately none of these options is that they don't do anything about ocean acidification.)
Objects in space are generally also subject to less weather, and as such they don't materially degrade. You could make a shield out of opaque film that would tear to shreds at the slightest breeze (see JWST sun shield)
We do not have decades to develop a mature space-mining and construction industry.