Well, I think they could have started counting earlier and made it unsigned. The whole negative time is like a hack: they added it to represent earlier dates after the date functions had been finalized.
Well, sure, using signed numbers solely to represent dates before 1970 is not a good idea. But signed time_ts have other benefits, as described above. It allows -1 to be an error value (though -1u could be in case of unsigned numbers), and differences in time (even negative differences) to be represented more easily.