Ubuntu core is meant to be a VERY light OS, which is ideal for RPI zero.
It's no "lighter" than Raspbian lite in terms of e.g., RAM consumption -- which is really a matter of how you configure the system, not the distro you choose.
It may be lighter in terms of how much space the base image requires (Raspbian lite is ~1.8 GB), but since you provide the SD card, this has nothing to do with which model you use. You could put a big card in a Zero just like you could put it in a 3B+.
What is the reason for not enabling it to be installed on Rpi Zero ?
Because the single core Pi's have an ARMv6 processor, which was arguably a bit outdated when the Pi was released (it was in fact 10 years old in 2013 -- ARM1176JZ(F)-S is the ARMv6 implementation used).
All of the existing Pi distributions, including Raspbian, are essentially tweaks of parent distributions that were not created specifically for the Pi -- they are for generic ARM targets. I believe the only GNU/Linux outfit to maintain an ARMv6 distro is Debian, and this is what Raspbian is based on.
Most of the GNU/Linux organizations, including Ubuntu, have ARMv7 distros, since there are many more ARMv7 devices around (including the multi-core Pis). But they do not have an ARMv6 one.