It's also a complete idiocy to possibly not copy everything. I've never wanted that. It's begging for bugs. If there's not enough room to copy all the source bytes, you either know that in advance or you want to crash hard.
Even memcpy itself is hardly necessary as a library function. It's a simple loop. But at least it's what you would write anyway, and in some cases compilers are able to optimize it (with questionable benefits).
Moreover, most of the time I’m either certain the output buffer is large enough (maybe because I just allocated it) or I really do want the output buffer to have a truncated string. Strncpy’s two dumb behaviors that I almost never want is to pad the destination buffer with zeros if the source string is smaller and to leave the destination I terminated if the source is longer.