I don't claim to be an expert on this, but I think it may be because that while tonogenesis is a "special" process, in that it produces a whole new dimension to the phonology (as opposed to something more "trivial" like clusters becoming new single segment phonemes), whereas tonoexodus seems to not be much different from other processes of loss in segmental contrasts. Yes, a sudden collapse of the tone system in a Chinese language, or any other language with a high functional load on tonal contrasts would be rather challenging to deal with, but so would any sudden collapse of significant scope, whereas a slow collapse, where contrasts are lost slowly, one after one, in some environments before others gives plenty of time to resolve any disasterous mass ambiguity with innovations.
I have tried looking around for examples of tone loss, and this seems to be the pattern I have been able to find. The Oto-Manguean languages with fewer tonal contrast that the reconstructed protolanguages seem to simply come from mergers of tones, either consistently or only in some environments (e.g. unstressed syllables) though the data is not quite clear.
Classical Chinese had 8 tonal categories divisible into yin and yang registers occuring respectively after voiced and unvoiced consonants, and into four different categories, ping, shang, qu and ru(checked syllables). While some modern lects such as Songjiang maintain all of these as seperate categories (Songjiang also retains contrastive onset voicing), others collapse the system in various ways. Beijing Mandarin collapses the yin/yang distinction of the shang and qu tones and merges ru into the other tones, while the relatively nearby Tianjin Mandarin keeps yin shang seperate, while merging yang shang with other tones. Along similar lines the different Chinese lects have radically different distinction-dimininshing sandhi processes, from the well-known relatively limited
214 > 35 / _214 rule of Beijing Mandarin to the complete loss of surface realisation of all but one dominant lexical tone in Northern Wu variants such as Shanghainese. Again, there does not seem to be any phonological compensatory measures associated with any of these losses of contrasts.
Tonoexodus that isn't a simple collapse seems to be hard to find, though the Danish glottal suprasegmental feature stød likely originates in a pitch accent system (note that some dialects have pitch-accent and some collapse the distinction entirely), and it seems reasonable to expect that other collapses of a two-way tone system to a phonation system could be found. As for other things, the largely autosegmental nature of tone means that it doesn't leave much room for other segmental changes, however there seem to be a few cases of such influences, primarily on consonant voicing discussed in sections 2.6 and 2.7 of Yip's Tone and references therein, though she notes that it has been argued by Thurgood that all such alternations are a product of phonation types (which may then coincidentally be associated with tone) influencing voicing rather than tone itself.
In conclusion it seems that the most likely process of tonoexodus is simply a slow gradual loss of contrasts in an increasing number of environments, with the associated lexical replacement/innovation that comes with language change, and a tone system evolving into something else rather than just being lost entirely is likely to become a phonation system, possibly with a minor influence on consonant voicing as well.