Using the past to explain the present
We must begin by accepting, in the face of the evidence presented above, that there is no way of making the vowels conditioning [r]-Insertion synchronically principled; they do not share any feature, with [r] or with each other, which would make context and output a natural class. In short, [r]-Insertion is indeed synchronically arbitrary, as its critics allege. However, if we consider [r]-Insertion diachronically, and accept that insertion is a result of prior deletion, there is nothing arbitrary about it at all. From the historical point of view, the structural description of [r]-Insertion makes perfect sense.

Recall that the eighteenth century sound changes of Pre-/r/ Breaking and Pre-Schwa Laxing (shown in (Non-rhotic /r/: an insertion analysis) above) meant that /r/, at the time of /r/-Deletion, could only appear, in the incipiently non-rhotic dialects, following a limited set of vowels. For the ancestor of RP, this set consisted of [ɑ: ɔ:], schwa, which may be the second element of a centring diphthong, and [з:], which we may think of as long schwa. Further optional smoothing adds [ε:] to the set, although this does not greatly affect later developments, since there are no English words with final [ε:] which do not also have etymological following /r/. These vowels, and some example words, were listed in (Alternative analyses). Since [r] could occur only after these vowels, and since it was the consonant deleted in these environments (there being no parallel or alternative process of [k]- or [m]-loss, say), it follows that [r] should be inserted after the same vowels, as a function of rule inversion. In cases where vowels from this set appear finally in words lacking historical /r/, the new process of [r]-Insertion will then regularly provide [r] when any vowel follows, leading automatically to intrusive [r]. This historical connection seems to have been obscured by the fact that the rules of /r/-Deletion and [r]-Insertion do not look like exact inverses when written, as shown in (1).
(1) 

Obviously, the input and the structural change are inverses: [r] and zero change places. However, the problem lies with the rest of the structural description; whereas V and the disjunction of C and pause clearly are opposites (if something happens before vowels, it precisely does not happen before consonants and pauses, and vice versa), the absent left context in the deletion rule has been replaced for [r]-Insertion by a particular group of vowels which, as we know, will be different for different varieties. It is, of course, nonsense to argue that /ɑ: ɔ: ə/, or any other subset of vowels, is the inverse of zero, and phonologists have therefore tended to assume that the left-hand environment for insertion has appeared either by accident or by sleight of hand on the part of fans of insertion rules. In fact, the solution is deceptively simple: the left-hand context for deletion does not have to be written. It is the succeeding consonant or boundary which conditions deletion, and the preceding context would simply consist of the entire set of vowels after which [r] could, at that time, appear. The issue of cross-dialectal variation in the set of conditioning vowels is also easily resolvable: in West Yorkshire, the inventory of vowels and the quality of low vowels is rather different from that of RP; thus, the vowels after which [r] deleted, and after which it is now inserted, are likely to vary to some extent. Finally, the introduction of this historical viewpoint resolves the quarrel over what conditions what in modern non-rhotic varieties: does /r/ have some effect on preceding vowels, or are the vowels responsible for the presence or absence of [r]? Well, both: that is, although /r/, or more precisely a complex of sound changes associated with it, did historically alter the quality and quantity of preceding vowels in ways we shall explore further below, it is now that resulting set of residual vowels which governs the realization of [r]. All this means that the set of vowels conditioning [r]-Insertion is precisely predictable in historical terms ± the present-day reflexes of the vowels after which [r] could appear at the time of deletion, are those which will trigger insertion in any given dialect. Nonetheless, this set of vowels remains arbitrary synchronically, depending as it does on the course of particular sound changes in particular varieties of English.