Agreed, and this may be a situation in which abbreviations are to some extent our friend. Whenever it seems possible, appropriate and likely to be understood, I try to use "L" (or "switched L" or "permanent L"), in an attempt not to confuse DIYers etc. but, at the same time, to not feed those clever clogs who are prone to jump in with comments about 'strictly correct terminology'While what you say is strictly speaking true using "Line" for the wires that are 230 V above Earth potential is confusing for the average DIY reader. Like wise calling the Neutral wire Live is also confusing for the average DIY reader.
In fact, I'm not really sure what the 'strict definition of "Live" really is. BS7671 says:
It doesn't define ';energize(d)', so I'm left with having to assume that it refers to any conductor or any 'part' which is not 'intended to be' at earth potential - but that's just a guess! It's also a little odd (confusing?) that, in a TN-C-S installation, the conductor providing the 'return path' back to the transformer is called a 'Live conductor' within the installation, but then ceases to be a 'Live conductor' once it is upstream of the cutout!Live conductor (see Live part).
Live part. A conductor or conductive part intended to be energized in normal use, including a neutral conductor but, by convention, not a PEN conductor.
Kind Regards, John