Post History

Grammatical categories are just tools to decompose a language into very simple, independent processes and rules that can be studied separately.  But the actual language is much more convoluted than just a vocabulary and some universally applicable grammar rules.

Let's take the English word "can".  Its infinitive either doesn't exist at all, or it takes the highly irregularly derived form "to be able to".  (The first approach is traditionally [preferred](https://en.wikipedia.org/wiki/Defective_verb#Common_defectives) by grammarians.)

Non-passive binyanim are normally described as word derivation processes (because they are semantically non-transparent: you can't fully predict what a stem means just from the binyan and the root; and because they are non-productive: the stems are fixed, speakers of Hebrew aren't deriving new ones on the go, and if they do, they risk a misunderstanding). Infinitive formation is normally described as an inflection process, and that surely suggests that you should be able to create an infinitive from any verb, including pu'al and huf'al.  Alas, like with modal verbs of English (see the example of "can" above), those binyanim are grammatically defective, and there's no infinitive nor imperative, and only some of the tenses are available: English modals have present and past tenses but no future tense forms, pu'al and huf'al have only past and future tenses, but no present tense forms.

There seems to be some debate regarding whether binyanim are derivational or inflectional.  (See for example Mark Aaronoff, [Morphology by Itself: Stems and Inflectional Classes](https://mitpress.mit.edu/books/morphology-itself) who seems to be approach the "non-passive" binyanim among themselves differently than the "active-passive" contrast.)

OK, so far I'm just saying "those words don't form an infinitive, live with that".  However, I think that I just found a hint of an answer to your question in Doron's [draft paper Binyanim - form and function](http://pluto.huji.ac.il/~edit/papers/EHLL.Binyan.pdf):

> The marked binyanim,
the causative _[hifˈil/hufˈal]_ and the intensive _[piˈel/puˈal]_, express the thematic role of the verb's subject: cause
and agent respectively. The simple binyan _[paˈal/nifˈal]_ functions as default and is neutral as to the
subject's role.

Well, by definition, an infinitive is the word form which does not _have_ an expressed subject.  So it should better be neutral as to the subject's role (or [thematic relation](https://en.wikipedia.org/wiki/Theta_role)).  No wonder that pu'al and huf'al don't form infinitives, but nif'al does.  Taking the root כּתב, you can create a passive infinitive using nif'al just fine: להיכתב, "to be written".

She continues:

> But there are many roots which derive singleton verbs, verbs which do
not contrast with an equi-rooted verb in another binyan or with an equi-rooted noun/
adjective. There is no contrast associated with such roots, thus no meaning emerges;
the binyan is sometimes arbitrary, and often dictated by phonological considerations. 

Well, I think that some of these words perhaps just have had some bad luck in choosing which club to join.  If you want to form the infinitive, imperative, or present tense from these words, you may need to find another way to express yourself.  On the flip side, the words often gained easier pronunciation of the forms that do exist (Doron says).