For example, someone discover security vulnerability in Vesta php script, makes bot that will scan all IP rangs, find all Vesta servers, and makes massive hack of all servers.
With secret url, hackers will not find your myVesta server.
If someone find security vulnerability we will fix it immediately, so there is no time for your users to hack you, even if they have high hacker skills

It is absolutely safe to give someone your secret URL, it's just a link that will open login form of myVesta.
He can not hack you with that URL.
With secret url, he will just be able to load login form of myVesta.