I'm late to the party, but anyway: I think you're somewhat misunderstanding/ misrepresenting his proposal. As I understand it, his idea is that a precursor of Slavic was already spoken, though mostly as a second language, in the region of the Avar Khaganate, but the political unity of and increased mobility under the Avars helped to spread and consolidate it, and contributed to people switching to it as their native language. For further context, he seems to adhere to the Balto-Thracian hypothesis, i.e. the idea that Thracian (and Dacian) are closely closely related/ part of Baltic/Balto-Slavic. This isn't a consensus among historical linguists, but it's not new, or his idea alone, see https://en.m.wikipedia.org/wiki/Baltic_languages#Thracian_hypothesis
So with this background, what he seems to be saying that Proto-Slavic emerged as a lingua franca sometime before the Avars (maybe in Hunnic times), but more a koïne than a pidgin, with most of its original adapters speaking closely related Thracian, Dacian and Baltic languages, later joined by speakers of more distantly related but also highly inflected languages (Balkan Romance, East Germanic, Iranian,...). When the Avars, whatever language they originally spoke (I don't think we can presume it was Turkic, at least not for all of them), arrived in the Black Sea region and later Pannonia, it would have been the natural choice to adapt that language to communicate with their neighbours and subjects out of practicality instead of learning five or six languages.
It should be said that the Avars probably weren't very numerous, and possibly weren't linguistically homogenous even when they first showed up in Europe. The "standard theory" is that the original Avars were the warrior elite of the Rouran Khaganate of Mongolia and Manchuria who went West to escape subjugation by the Gökturks. There is no reason to assume the Rouran empire itself was linguistically homogenous to start with - they may have been a conglomerate of Turkic, Mongolic, Tungusic speakers from the get go and even could well have included speakers of languages that no longer exist, but they certainly weren't monolingual by the time the crossed the Carpathians. If I recall correctly, some contemporary or near contemporary Byzantine source says that when they crossed the Carpathians, they numbered 100,000, of which 20,000 "true" Avars, the rest presumably people from the Black Sea/Lower Danube region (Thracians? Sarmatians? Goths? Huns? Will we ever know?). The absolute number may well be exaggerated, or a wild ass estimate, but I don't see a reason to assume the proportion is way off. Under this hypothesis, many of the "Avars" in Pannonia would have been familiar with the region's lingua franca from day one, as well as most of the resident population - and quite a few would have spoken a closely related language at home. Certainly in the later part of the Avar period, "Avar" was more a politiconym than an ethnonym - an Avar was an arms-carrying member of the Khaganate's elite, not someone speaking a particular language or worshiping a particular set of gods. Of course, among that elite, a dominant East Asian ancestry would still have been more widespread than among commoners, but I don't think apartheid era South Africa or pre-Civil War Dixieland make a good model for Avar-era East Central Europe.
I'm not saying he's right, just what he actually seems to be suggesting is much more plausible than you make it sound.
I do think that a weaker version of the hypothesis is very plausible: That Balto-Slavic never split into a Baltic and a Slavic branch, but rather that by the time ProtoSlavic became different enough to warrant summarizing the non-Slavic variants of Balto-Slavic as "Baltic", "Baltic" had already split into several languages of which the ancestor of Proto-Slavic was originally but one, and that the rapid linguistic change Slavic was undergoing that made it stand out among all others was in no small part triggered by language contact. Plausibly also that the high degree of uniformity Slavic maintained a it was spreading suggests not just a one-way expansion from an "Urheimat" but a large degree of mobility in all directions within the area where Slavic was establishing itself - otherwise we might expect it to be accompanied by rapid differentiation which is apparently not the case.
Caveat: I'm just a mere syntactician-turned-programmer with an interest in early medieval history, not any kind of historian, historical linguist, or slavicist. I do not consider myself qualified to speculate which languages were most instrumental in said contact scenario and how closely they were related to Baltic/Balto-Slavic, or what political circumstances facilitated the mobility and cohesion of early Slavic during its spread, or how much of that spread was actually due to language shift and how much due to migration. I do think that the apparent cohesion of Slavic precisely at a time when you'd expect divergence due to geographical distance and the influences of very different substrate languages requires an explanation.
Arguably though it works the other way around too: if Slavic was highly uniform, that could have facilitated its use as a lingua franca: if East Germanic and West Germanic were already different enough to hinder mutual intelligibility between Gepids from Transilvania and Lombards from Bohemia, both of them switching to the idiom of their new Slavic neighbours could help them communicate, much like Poles and Croatians today tend to switch to English, so Slavic could have become a lingua franca partly because it was uniform.
(I'm basing my interpretation of his claim on a cursory reading of this paper and I haven't read anything else he wrote on the topic: https://www.academia.edu/227792/The_Slavic_lingua_franca_Linguistic_notes_of_an_archaeologist_turned_historian_ )