Why does Banded Needleman-Wunsch give alignments with no more than d base pairs of indels?
You are correct, the number of insertions/deletions $d$ is not constrained (only) by the bandwidth. 

However, the algorithm only uses the fact that if we know $d$, then the path must stay within the $2d+1$ band. This band does not have to be tight: a zigzag path would indeed fit within a much narrower band. 



You may wonder why the smallest bandwidth (which is indeed equal to the maximum sum over prefixes of your list $L$) isn't used as a parameter instead of $d$. Since $d$ is related to the similarity of the strings, it isn't unreasonable that an upper bound of $d$ is known in some applications. The smallest bandwidth doesn't seem to correspond to a 'natural' parameter in the context of similarity as $d$ does, so it doesn't seem reasonable that it is known and can be used in the algorithm.