There are a number of reasons using ADS-B's frequency as a carrier for voice communications isn't a great idea. There are a few issues and factors which I believe you're not taking into consideration which, once understood should illustrate why that is not a workable or desirable solution.
First, I'm not going to address this in terms of the UAT system, the fact that it's only used in the US would proclude it's use anyway.
Now, the frequency that ADS-B operates on for transmitting digital data packets is 1090 Mhz. When ADS-B was first designed, in order to minimize the complexities inherent to any work integrating a newer, more modern data transceiver system into an older existing system, eliminating any need for additional frequencies which are only compatible with the new gear, and this would require additional system components to translate or retransmit, is always a smart move.
In the case of ADS-B, the system engineers decided to use an existing frequency by simply building the entire ADS-B system essentially over the existing Mode-S transponder Secondary Surveillance Radar (SSR) systems. In fact, for a short time way back when, an ADS-B signal was actually referred to as Mode-S ES signal, or Mode Select - Extended Squitter signal. The Squitter being the colloquial term for a Mode-S data packet. Therefore, if one wants to fit more data to send, just extend that squitter. Tada!!!
While the Mode-S system does reduce the frequency congestion when compared to the previous generations of transponders (Mode-A/3/C), one of it's primary design goals, even without all the ADS-B noise being added to the frequency, trying to for a voice carrier onto the same frequency would certainly be less than ideal.
Additionally, adding voice coms, even in digital format, would inevitably begin to cause interference with the SSR and transponders exchanging data, so there's that.
When you consider that we haven't even broached the fact that all the air carriers, who are required to be equipped with and operating with a Traffic Collision Avoidance System (TCAS). Wanna take a shot and guess which system TCAS is built on top of? That's right, Mode-S.
I've never heard what it sounds like, but I've got to imagine that when 2 TCAS boxes start chatting feverishly about who goes high and who goes low so they don't collide, it's not a pleasant sound. And these are REALLY important communications which should not be interfered with, cause if you've got 2 TCAS talking to each other, best to let them finish the conversation!!