Remember, the codec has to handle less than 20 ms latency. Running a sizable ANN (fast) or HMM in that time is not easy or even possible. A small one will be no good for various speakers.
Instead the codecs use various specialised error hiding tricks and adaptive strategies.
Heck, Codec2, one of the strongest voice codecs around could be used if all else fails. It is beginning to be used in SDR and amateur radio - optimised for availability and intelligibility not quality. It would be nice to have a variant integrated with CELT for higher quality.
Our pbx is hosted by http://sipworxx.com/ and it works great.
I use this with good Polycom "HD voice" devices. I'm also rather picky about voice quality.
Grandstream, Yealink, etc. all provide pretty easy to administer Asterisk-based PBX appliances that can be paired with a SIP trunk of your choice (shout out to Flowroute here, they're great).
If you're feeling more adventurous sipXecs from sipfoundry is pretty easy to configure relative to the additional complexity it brings over the more simplified alternatives. I went from having 0 real world experience with SIP to managing a small installation for my aunts shop as well as one at home in a couple days.
For proprietary offerings there's of course Skype for Business, etc. and I would argue they aren't terribly hard to configure or maintain either.
Most of the work is just in network configuration once you have multiple sites and you need to ensure QOS going over your MPLS or whatever to ensure your voice packets take priority - that can be more difficult but that's something a competent network admin can help you with.
Edit: "canbe"