There are two main senses in which people speak of conjugations (as countable things). One is (seemingly) arbitrary lexical classes such as -er, -ar, -ir verbs in Spanish. The other is classes of formal distinctions made, such as past, present, future, perfective, negative, focus etc. Such as there is a generally accepted theory, it would be that languages tend to eliminate things that have to be memorized, where there is no discernible rule. (The tendency can easily be resisted, as in the conjugation of "be" and "go").
Languages also tend to develop "constructions" where the meaning of two words put together isn't literally the sum of the parts, for example "have bought" isn't just the meaning of "have" plus the meaning of "bought", so you have to also learn a new rule for interpreting the construction. When this is coupled with some kind of phonological reduction of one of the parts, you get "grammaticalization" and the creation of a new conjugational parameter. These two trends, which are also common in languages, encourage an increase in the number of conjugations, and IMO reflect something about the nature of word-formation versus sentence-formation (that more arbitrary facts of combination and interpretation should be registered in the morphology, not the syntax).
I am not aware of any in-depth empirical study across human languages that counts the likely historical increase in distinctions (for example in Bantu verbs) vs. decrease (as in most Indo-European languages or Arabic).