Three people is the minimum viable democracy: the smallest number for which a majority is possible.

This principle is used all over robust engineering, from Raft to best-of-three sensors.

You only need 1 witness for that. The first two are the parties.

3 is an enhancement for redundancy. Habit an odd number is a false confidence. Think about it: what happens if you have 4 witnesses? They could tie? How is that worse, as it adds more information that maybe 2 of the first 3 are lying or wrong?

Having just the notary there relies on trusting the notary to be an impartial party, with just one witness in addition to the two parties there's only one point of verification meaning only one person you have to corrupt to be able to lie about what happened. Bringing in more people increases the size of the conspiracy required to lie about the transaction.

An alternative to blockchains, Corda does something similar instead of the wasteful proof of works.