Why are Proto-Slavic nasal vowels reconstructed as ę and ǫ? But not "i with a little tail" and "u with a little tail"?
Nasalized į, ų, and ą are also reconstructed for the earliest stages of Proto-Slavic, but they merged into other vowels before the Common Slavic period.
- PBS *lúnˀka "bast" (*) > *lų́ka > Common Slavic *lỳko > Russian лыко
- Compare Lithuanian lùnkas
- PBS *deśimtas "tenth" > *desįtu > Common Slavic *desętъ > Russian десятый
- Compare Lithuanian dešim̃tas
- PBS *źambas "tooth" > *zą́bu > Common Slavic *zǫ̂bъ > Russian зуб
- Compare Lithuanian žam̃bas
(*) Fiber made from the inner bark of a tree
EDIT: For a reference, Alex B offers this quote from Kim (The phonology of Balto-Slavic, 2018):
Sequences of tautological vowel + nasal yielded nasalized vowels, with *iN, *eN > *ę and *uN, *aN > *ǫ.
In other words, ę and ǫ are the only nasalized vowels that survived the various vowel mergers in Proto-Slavic; sequences -iN, -uN, and -aN existed in Proto-Balti-Slavic and nasalized early in Proto-Slavic, so it's really just an accident of fate that we don't end up with į, ų, and ą alongside ę and ǫ.
I am answering only the question in the title. I will not touch ų and others that merged with the reat according the answer why Draconis. I will explain the reasons for interpretting ⱗ and ⱘ as ę and ǫ. Even the shape of the letters is telling in comparison with ⰵ and ⱁ.
The reasons are for the reconstruction are both etymological (e.g. nom. ramę vs gen. ramene, pontĭ > pǫtь - cf. Latin pontis, borrowings like *kuningaz > kъnędzь, ganisan > goneznǫti,). These show that both en and in gave ę and that both an end on gave ǫ.
... and through written words in the Latin script. E.g.
Wenceslaw - Vęceslav (Václav, Věnceslav, Wenzel) in the 10th century
The earliest stages of Protoslavic are reconstructed before the nasals emerged from full "en" "on/an". E.g.
early PS nom. otrokent, gen. otrokentes
OCS nom. отрочѧ, gen. отрочѧте
(by Vepřek, Komparativní tvarosloví staroslověnštiny a staré češtiny)
ǫ and u are already confused in the Prague fragments (pomilǫi), but that is much later.