The main problem with stop words is not the index size - but the quality of the answer. They tend to be dominant (have very high tf value and thus might make the results returned wrong), and not the size of the index.
In any case, indexing stop words does not increase the size of the index significantly (and it definetly does not "explode")One way to overcome it is to use the stop words (and not omit them completely) when indexing n-grams. I don't know if it actually being done, but it definitely can help improve the returned results.
Also: stop words are not always* omitted. In sarcasm detectors, for example - it seems (empirically) stop words are very significant to the answer.