In the next four years or so do you think that technically is possible that bitcoin privacy problem will solve and coin mixing companys will not be needed again.
No, because I don't think the Bitcoin network will ever reach a satisfactory level of privacy. Chain analysis companies such as Elliptic have achieved deanonymizing lots of users and therefore, diminish the anonymity of us all. So, even if some can accomplish hiding their footprints, they may get traced due to the carelessness of the rest. It's either a full-scale upgrade in a protocol level or no feeling of true privacy at all.
And if it ever does achieve this level of privacy, I doubt the governments will just sit back and let it happen. At least now they do have a supposedly close watch. Anyway, not at present, but food for thought.