This is a bit of a thought experiment, so it may be not entirely correct (especially the maths – my probability theory is very rusty).
One of the lesser reasons for using the DNS rather than IP4 addresses is that typing mistakes are more easily caught – if you intend to type 192.168.67.52, but accidentally enter 192.168.67.53 instead, you still have a valid IPv4 address. Whereas entering the domain name wombar.example.com instead of wombat.example.com will most likely get you an error instead of sending your secrets off to an unknown location on your network – unless you have a rather silly server naming convention of course!
But how likely are you to make a mistake typing in an IPv4 address? According to a random web site “out there”, the average accuracy of a typist is 92%, or an average of 8 typos per 100 characters. If we convert this into a probability, we get a probability of typing each character correctly as 0.92.
Given that typing IPv4 addresses is something that some of us have a lot of practice at, and in many cases we will notice typos before they become a problem, I’m going to arbitrarily declare that the probability of getting any character within an IPv4 address correct is 0.999. But to type in an IPv4 address correctly we have to get a maximum of 15 characters correct :-
So the probability of getting all those characters right is 0.999 (first character) x 0.999 (second character) … Or 0.999^15.
And once you work that out, subtract it from 1 (to get the probability of making a mistake) and convert it into a percentage, there is an 11% chance of making a typo in an IPv4 address.
For an IPv6 address such as 2001:db8:ca2c:dead:44f0:c3e9:28be:c903, which has 38 characters (no I’m not doing that silly table for IPv6) – 100 * (1 – 0.999 ^ 38) – 32%.
Now whilst my calculations may be a bit off, the likelihood of entering an IPv6 address incorrectly is nearly three times higher than the risk of entering an IPv4 address incorrectly.
In other words, with IPv6 you really need a good working DNS solution just to keep the errors to manageable levels.