Yeah, living in (and specifically being born in) a place that considers itself an independent country but not recognized as an independent country sucks for a lot of reasons but one is travel:
Right now a kid born in Transnistria could get a Transnistrian passport issued to them, but there aren't any countries that recognize Transnistria as a country (with the exceptions of Abkhazia, South Ossetia, and Artsakh all of which arguably aren't countries themselves), so that passport won't let you go anywhere (except Abkhazia, South Ossetia, and Artsakh). Hence the strong incentive for folks living in the region to find a way to qualify for passport citizenship in some more generally internationally recognized country.