Because they're fundamental operations.
By the same line of thought, you could argue that addition has few real-world uses, since it can be replaced completely with subtraction (and negation) and multiplication. But we keep addition because it's a fundamental operation.
And don't think for a moment that just because you haven't seen much need for bitwise operations doesn't mean they're not used very often. Indeed, I've used bitwise ops in nearly every language I've used for things like bit masking.
Off the top of my head, I've used bitwise ops for image processing, bitfields and flags, text processing (e.g., all characters of a particular class often share a common bit pattern), encoding and decoding serialized data, decoding VM or CPU opcodes, and so on. Without bitwise ops, most of these tasks would require many times more complex operations to perform the task less reliably or with poorer readability.
// Given a 30-bit RGB color value as a 32-bit int
// A lot of image sensors spit out 10- or 12-bit data
// and some LVDS panels have a 10- or 12-bit format
b = (color & 0x000003ff);
g = (color & 0x000ffc00) >> 10;
r = (color & 0x3ff00000) >> 20;
// Going the other way:
color = ((r << 20) & 0x3ff00000) | ((g << 10) & 0x000ffc00) | (b & 0x000003ff);
Decoding CPU instructions for RISC-type CPUs (such as when emulating another platform) requires extracting portions of a large value as above. Sometimes, doing these operations with multiplication and division and modulo, etc., can be as much as ten times slower as the equivalent bitwise ops.