It depends on what you mean by "most". While it is true that Google, Amazon, Baidu, et al. have a DNN-based implementation, most open source ASR systems (eg. CMU Sphinx, HTK, Julius) are still HMM-based. There are still very few DNN based modern speech recognition systems available to developers. Most are behind a cloud API. Mozilla runs one: https://github.com/mozilla/DeepSpeech/
I think the discrepancy lies between "open source" and "modern" in this case. It is true that DNNs outperform traditional HMM models, but speech recognition systems are complex. It's not trivial to simply "port" an existing open source system to switch to DNNs if you don't have the manpower and training data that Google and the like possess.
There is no contradiction here, state of the art systems use both DNN and HMM (Kaldi, for example). It is GMM (Gaussian mixture model) that was replaced by DNN, HMM is still here.
This not correct. Most modern speech recognition systems are based on deep neural nets (DNN).