The entire Bloom filter is a loss in terms of space. The Bloom filter may give me better lookup performance (by skipping lookups in the underlying data structure) at the expense of this space. But this is if the Bloom filter itself is fast.
I think you're getting a few things wrong. Bloom filters do not serve as data structures for faster lookups, on the contrary, other approached perform probably much better. Bloom filters are only useful because of their low space complexity. E.g. look at genome assembly https://en.wikipedia.org/wiki/Bloom_filters_in_bioinformatic.... Storing and looking up every k-mer is super expensive (memory-wise). Bloom filters allow for efficient k-mer lookup, without actually having to store all the possible k-mers in memory.
