> companies get the vote based on number of employees

That is the result of recent legislation. Until about 20 years ago companies did not get votes. Individuals got votes by being freemen of the city, usually by being members of a livery company, the descendants of medieval guilds.

> Can’t easily be changed because some of the “rights and liberties” predates written common law and are “senior”.

It can be changed by passing legislation.

I lived in the city (in the Barbican) in the early 2000s and loved it.