Common descent vs. waves of areally shared innovations are also not the only ways to explain similarities between languages. For one thing, I think historical linguistics has probably not considered preadaptations anywhere near well enough.
A simple example: if we look at the history of the Indo-European languages, we’ll find that affricates seem to be very unstable and prone to lenition into sibilants (*ts > /s/ has happened separately in at least four areas: Romance, Slavic, Iranian, and parts of New Indo-Aryan; also Albanian, but that might be areally linked to either Romance or Slavic). But, if we look at Uralic instead, we’ll find that affricates actually tend to be somewhat stable (e.g. in the Mordvinic languages, word-medial *-č- remains unvoiced, even though *-p- *-t- *-k- become voiced and *-b- *-g- then spirantize further) or can even undergo fortition (e.g. Finnic and most of Samoyedic shift *č > *t).
This is not a mystery if we also look at the general phonological outlines of the two families. Indo-European started off with only a single sibilant *s (and Middle Indo-Aryan likewise merged Old Indo-Aryan ś ṣ s all again into just /s/), versus an extensive inventory of stop consonants (set in a 3×5 grid), while the Uralic languages started off with tons of sibilant consonants hanging around (*s *ś *š *ć *č) and only the most bare-bones stop system (*p *t *k, with *t also fairly rare). So Indo-European languages have had more room for affricate > fricative shifts than Uralic languages; and inversely Uralic languages have also had more room for affricate > stop shifts.
For a more complex example, consider the reduction and loss of unstressed vowels. Looking at the Germanic languages might suggest that this is a natural result of word-initial stress; but, if we survey a bit further, we will find that e.g. the Finnic languages also have word-initial stress — but almost none of them have vowel reduction, and none of them have general apocope (loss of word-final vowels). Several, however, have a curious pattern of apocope that is restricted to words with three or more moras (this applies in at least four separate areas: Estonian; Ludian-Veps; Southwestern Finnish; a few dialects of Ingrian).
The lack of vowel reduction in Finnic can be accounted by them having vowel harmony instead: this already has the effect of restricting the contrastive load of vowels in unstressed syllables. Allowing the vowel combinations /e-ə/ (front+reduced) versus /o-ə/ (back+reduced) is a two-way contrast in the first-syllable, versus no contrast in the second syllable; but allowing /e-æ/ (front+front) versus /o-a/ (back+back) is really quite similar: we again have only a two-way contrast, which can be uniquely determined on the basis of the first (stressed) vowel.
The mysterious Finnic tendency for conditional apocope also has an explanation: Finnic doesn’t just have initial stress, but also notable secondary stress on odd-numbered non-final syllables. In other words, Finnic languages prefer to divide words into trochaic feet (one stressed + one unstressed syllable) whenever possible. This means, for example, that a trisyllabic word like *vásara (‘hammer’) is going to be under pressure to be reduced into the trochaic shape /vásar/, while a bisyllabic word like *vasa (‘calf’) is not.
(I’m skipping over how moraic consonants fit into this — why are words like *vasta still prone to apocope — but it also follows, through some additional details, from allophonic features that can be assumed to be present already in Proto-Finnic.)
These are both examples where we have a preadaptation (size of the sibilant system, lack or presence of secondary stress) that is itself a result of common inheritance — however, in principle preadaptations can also come about as wave-like innovations. Maybe the expansion of pharyngealization in Afro-Asiatic languages can be an example: this is found as a fairly wave-like innovation that covers the Berber languages and the Central Semitic languages, and converts old ejectives like *tʼ *(t)sʼ *kʼ into “emphatic” consonants like /tˤ sˤ q/. (It strikes me as being itself partly conditioned by the presence of pharyngeal consonants /ħ ʕ/, but it also has a dialectologically and areally contiguous distribution that suggests some wave-like action going on as well.) However: this then creates a motivation for the introduction of further emphatic consonants like /bˤ/ or /lˤ/, that have no connection to earlier ejectives; something that has indeed happens in various Berber and Semitic languages, with no particular connection between them that I know of…