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Yes, but don't call it string library then. Strings should handle strings, and strings are unicode now. Unicode needs to be normalized and needs case-insensitive support. And it's not easy. I implemented the third of its kind. First there was ICU, which is overly bloated. You don't need 30MB for a simple string libc. Then there is libunistring which has overly slow iterators, so not usable for coreutils. And then the…
Why try to redefine the word "string?" In computer jargon I believe CISC and the PDP-11 have seniority. That's why all multi-word functions like memcpy are in C's string.h header.
I admit two words "string" and "text" are now interchangable. But that doesn't make strings have less requirements, people are just expecting more out of strings.