Reading official docs it’s obvious that PowerShell -match operator is more powerful than -like (due to regular expressions). Secondly, it seems ~10 times faster according to this article https://www.pluralsight.com/blog/software-development/powershell-operators-like-match.

Are there specific cases when I should prefer -like instead of -match? If there not, why at all should I use -like? Does it exist because of historical reasons?

See this explanation from Differences Between -Like and -Match

In a nutshell, if you are thinking, ‘I am probably going to need a wildcard to find this item‘, then start with -Like. However, if you are pretty sure of most of the letters in the word that you are looking for, then you are better off experimenting with -Match.

Here is a more technical distinction: -Match is a regular expression, whereas -Like is just a wildcard comparison, a subset of -Match.

So, whenever you are not sure what character classes, i.e. digits, letters, punctuation, etc., can there be inside, when you just want to match any character, you should be using -Like with its wildcards.

When you know there must be a digit at the start followed with 1+ sequences of a colon followed with alphanumeric characters up to the end of the string, use -Match with its powerful regular expressions.