It's not clear what your alternatives are - they seem to be the same. 'A pen is to write with' is just about OK grammatically, but very awkward - a native speaker would never say that. A more natural construction would be 'Pens are for writing with.' Note that it's more natural to use the plural form to talk about things in general. For example, if a child is sucking and chewing his pen, a teacher or parent might say 'Stop chewing your pen! Pens are for writing with - not eating!'

Non-action verbs (stative) verbs are often complemented with gerunds rather than to- infinitives. In your sentence the verb 'is' means something very close to 'exists', and to exist is not an action verb. So this is one of several complement patterns. Sometime these gerund complements take the form of a prepositional phrase and with some verbs the gerund acts like a direct object of the verb. I like fishing. - S+V+gerund (direct object) She is considering leaving her job. S+V(present continuous)+Object complement (gerund + object noun) Pens are for writing. S+V+phrasal complement (where writing becomes the noun object of the preposition) Notice that all of these verbs are state verbs and state verbs like gerunds as complements either as a direct object of as part of a prepositional phrase.