Businesswoman Hayley Parsons had already called for them to stand down before Davies did the same, while former Principality Building Society chief operating officer Rob Regan has offered to oversee an interim board.
In a statement, the WRU board did not directly address the calls for its members to resign but stated
The board also doubled down on its commitment to cut the number of professional teams from four to three by 2028, with WRU-owned Cardiff and privately backed Dragons set to be given licences.
That announcement has plunged the futures of Scarlets and Ospreys into doubt, with the west licence either being awarded to the Llanelli-based side or their Swansea-based rivals.
Asked whether he still had faith in those running the game in Wales, Williams, who coaches in west Wales, said: "No, I don't have much faith, to be honest with you. "
"I think we're still none the wiser.
"I think they just took a little break in deciding what was going to happen, but knowing deep down in their hearts that they wanted it to be three regions.
"We as coaches know the uncertainty of who's going to remain as a region next year and that is very difficult.
"But what we are trying to do and what we do need is a bit more support in the pathway side of the rugby.
"We talk about the regions, we talk about the national team, but where do they think these players come from?
"I can answer that for you straight away. That is schools and colleges. "
The WRU has been asked to comment.
