Here is the problem with these policies. What happens when just 1 person or 2 people have key knowledge?

My company has/had (the people I know with it left) this problem. Things hinged on one person and a team of effectively 1 or even 2 can never go on vacation.

Now, obviously this should be considered a problem too but other problems can make the 2/3 part unworkable.

I think the issue is that it was used as an excuse to deny vacation. It could also lead to everyone being put on teams of 2. Great, now no one can take a vacation by definition.

Not if your team size is two, for example.

My current team is 2 people. Should we never take a break?

No, because for some reason a lot of people take a lot of time off during summer.