Examples of languages with TAM inflection on pronouns: Hausa, Wolof
It is quite a rare feature but we find it in English as well: eg. we'll eat. we've sung. Imma do it.
From the English examples above, TAMs attach to pronouns very naturally as they are frequently right after the pronouns.
Perhaps TAMs have an extremely close relationship with verbs but not with pronouns?
Word order and degree of prefixing/suffixing definitely play an important role too. TAMs on SOV languages would look like German:
Ich-werde den Apfel (und so weiter) essen
As if it results in a long dependency length between werde-essen.
Is there any related research?