One peculiar aspect of Russian is the fact that some verbs simply don't have certain forms. For example, the verb "победить" doesn't have a first person singular future form. Even though, may I point out, the verb "угодить", for example, which has an identical ending, does have such a form, "угожу". Why isn't "побежу" allowed? Or "побежду"? I know, you are generally not supposed to ask why when discussing languages (especially if that language is Russian), but still: why can't Russian make certain forms for some verbs? Certainly, it should be a cinch for a language that is "great and mighty"
Why can't Russian make certain forms for some verbs?
Because these forms were perceived as defective (for various reasons) by some Russian speakers, and hence shunned.
This process is self-reinforcing: the less a certain form is used, the weirder it sounds when a speaker does try to construct it; and the weirder it sounds, the less it is used.
In case of победить, убедить the initial reason, most probably, was the possible homonymy with побежать, убежать for the form *побежу, and the discrepancy with the paradigm for рождать/рожу, угождать/угожу etc. for the form *побежду.
Both these forms are attested and have been in use, but neither got legs, so modern Russian uses the suppletive form одержу победу instead.
There are other verbs which lack certain forms: дерзить, сглазить etc. lack the first person present because of the homonymies; ощутить, очутиться etc. because of sound reduplication which is perceived as unpleasant to the ear; видеть, ехать, гнить etc. lack proper imperatives because they don't quite fit in any patterns, and so on.
If the want of a certain form poses a common problem, it's suppleted (like it happened with одержу победу, езжай and so on); if not, then it's just dealt with on ad-hoc basis.
I know, you are generally not supposed to ask why when discussing languages (especially if that language is Russian)
Linguistics is a discipline which is looking for the why behind the language evolution, Russian being no exception.
In some languages, the answers to these "why" questions are easier to obtain, because their evolution is more transparent (more written records, more descendant languages, more extant dialects); Russian is on the harder side.
But there's no law, at least not here on this site, that would ban you from asking.
Certainly, it should be a cinch for a language that is "great and mighty"
I'm not really sure how "greatness" and "might" of a language, whatever it means, are defined by its ability to fill conjugation tables in a uniform way. Any widely used human language is rife with different kinds of irregularities.