Ehm i looked up the distribution beforehand, see my edit. These things are not distributed evenly - you have a few surnames with an insane amount in relation to any others before even coming to homophones which tilt the balance even harder towards those supercommon surnames. Smith and Brown are the ones you would have real issues if using the suggested unique name schemata.

Edit: There's a whole another issue with this approach. If we do this on a per-country-basis, people moving into foreign countries will have to add the country of birth to everything, for example doctors appointments, for the rest of your life in case of a name collision. Making the system work worldwide will exacerbate the issue with very common surnames, because these are not only common in a single country. (Even in the DACH-area the name Schmid/Schmied/Schmidt and so on, which is simply the german form of Smith, is one of the most common surnames)