If X can possibly afford the fees, it is much better to hold actual passports for both nationalities.
A country may require the use of its passport by its citizens when entering or leaving the country. The US is an example, although the practical penalty appears to be a delay and lecture.
On the other hand, some countries require the mandatory use of its passport by its citizens when at least entering the country. e.g. X wants to visit country A (and doesn't have country A's passport) and country A has visa requirements for country B citizens. In such a case X would need to obtain a country A visa on X's country B passport prior to travel. A real-world example is a dual US/PAK citizen traveling to PAK having just a US passport.
X may have a need to travel urgently to a country that permits visa-free travel for one of the passports, but not the other. The delay in either obtaining a visa or obtaining a passport after finding out about the need to travel may be inconvenient. In general, you cannot expect other countries to allow the travel benefits of being a citizen of country A unless you can present a country A passport.
Generally, not holding a passport does not exempt you from the obligations of a citizenship. For example, the US tax obligations of a US citizen are not affected by whether the citizen has, or has ever had, a US passport.
