There is nothing especially irregular about country names. Let me explain.
In Esperanto, some names for tools end in "-ilo", e.g. "tranĉilo", "muzikilo" and "kombilo", while for other tools there is a word root that already signifies the tool, so that the "-il-" suffix is not needed, e.g. "forko", "gitaro" and "broso". Similarly, some place names end in "-ejo", e.g. "lernejo", "kinejo" and "drinkejo", while for other places there is a word root that already signifies the place, so that the "-ej-" suffix is not needed, e.g. "universitato", "muzeo" and "restoracio".
The same applies to country names: Some are derived from demonyms (i.e. words that indicate the nationality of a person) using the suffix "-uj-" (or alternatively -i-"), e.g. "Germanujo", "Francujo" and "Ĉinujo", while for other countries there are word roots that already signify the country, so that "-uj-" is not needed, e.g. "Argentino", "Tanzanio" and "Usono" (you are wrong in calling "Usono" an outsider; it is a completely regular member of this group of country names). There is nothing more irregular about this than in the case of tool words, place words or any other semantic category for which there is an affix.
But why did Zamenhof not make all tool words end in "-ilo", all place names end in "-ejo" and all country names end in "-ujo"? Well, his goal when introducing these suffixes was not to mark all words of certain semantic categories with them, but to allow for the formation of new words based on existing word roots, so as to decrease the number of word roots that need to be learned. Some tool words can naturally be derived from the name of an action performed by the tool (e.g. a knife being a cutting tool), and in that case Zamemhof used the "-il-" suffix. But in the case of other tool-action pairs, it is more natural to view the action as being characterized by the tool than the other way round (e.g. to play the guitar), so Zamenhof introduced a word root for the tool.
When Zamenhof and other early Esperantists were coming up with Esperanto forms of country names, mainly based on internationally widespread names, they were intuitively doing something very similar: When the internationally widespread country name was closely related to a demonym that describes a historic people, they made the Esperanto word be based on the demonym. But when the demonym related to the internationally used country name was a new expression signifying a group of people that were identifying with each other mostly because of living in the same country and not becaus of ethnic ties, they prefered to introduce a word root for the country and to derive the demonym from it using the suffix "-an-".
So why then are country names often considered more problematic than tool words, place words etc? I think there are two main reasons for this:
- Country names are usually taught in one lesson, whereas tool words, place words etc. are spread out through many lessons, so the bi-categoricity is more visible to learners in the case of country names.
- Country names are often taught with the suffix "-i-" instead of the suffix "-uj-". Given that many country word roots also happen to end in "i" (e.g. "Ĉili/" and "Aŭstrali/"), this causes confusion. There are no place word roots that end in "ej" and hardly any tool word roots that end in "il" (I think "fusilo" is the only one), so no similar confusion can arise in the case of these semantic categories.
The second problem could be avoided by teaching the country names using the "-uj-" suffix and only mention the "-i-" suffix as an alternative (this is also the reason why I prefer the "-uj-" suffix).
Finally, what about country names ending in "-lando"? In some cases, like "Nederlando" and "Irlando", "land" is just part of the word root, and I don't see anything problematic with that. But there are also some country names, like "Pollando" and "Tajlando", where the word root "land/" is used after a demonym instead of "-uj-". This usage is indeed an irregularity. But note that there are only five countries for which it is very common to use "land/" instead of "-uj-", and only three or four other countries for which this is done by some speakers. It is always right to use the regular "-uj-" (or "-i-") instead of "land/" for these countries (i.e. to use "Polujo", "Tajujo", "Finnujo", "Skotujo" and "Svaziujo"). I personally actually only use these regular forms.