When are you claiming all this work on 1-1+1... ended? in the 17th century as in your original comment, or with Cauchy? Do you really dispute that Gregory in the 17th century claimed that not all series should be summable?

Sure, aspects of their work ended up being useful, but other times books and papers had results that relied on "theorems" that simply weren't true.

You seem to be saying that sloppy proofs of true theorems are not useful.