You might say that, but there's not much to support it. Reina injured his hip which limited his ability to turn, he's never been the same since. Mignolet's problems were clear when he arrived. Coaches don't turn flawed players into perfect ones, that isn't how it works.
What is telling is that Achterberg was the only member of the first team coaching staff to be kept on when Brendan Rodgers took over, the only one to survive the cull over the summer and looks set to repeat the feat now.
My guess is that people at the club know something you don't.
A good coach doesn't turn 'flawed players into perfect ones'. But they can turn good players into great or even 'perfect' players. Pepe Reina was a world class goalkeeper until Valero left
Here is a true story about Xabi Valero and Liverpool.
Most people know that when Rafa was sacked he stayed on Merseyside for a while. But not many know that Xabi Valero also stayed on Merseyside even when Rafa went to Milan (initially). Even when Rafa had a break before taking the Napoli job Valero stayed on Merseyside.
Reason being that Reina was trying to keep Valero as his coach. To a point when the Cancers were looking for a replacement for Rafa said that they would keep him on in the new Backroom team. But they hired Hodgson and he brought Mike Kelly as assistant manager and goalkeeping coach so no Valero. Valero eventually joined Rafa at Milan as 'video analyst' then followed him to Napoli. He's now coaching Casillas at Madrid.
He was hired as a video analyst at Milan because he also trained the strikers telling them how a goalie defends his box and what side they tend to dive during penalties. He trained under former Liverpool goalkeeper coach Ochotorena (who trained Dudek for the 2005 penalties in Istanbul).
Following 2 world class coaches in Ochotorena and Valero the club have had Kelly and Achterberg. I think it's safe to say that we have not had experienced coaches
John Achterberg did not have top flight coaching experience prior to being hired by Liverpool
Liverpool have not had a goalkeeper in world class form since Valero left Liverpool. It's no coincidence