Not really sure it's factually correct to say the Kings slow-play prospects. The Byfield situation is unique because they had the AHL available when it normally isn't for a teenager from the CHL.
Since this management/scouting staff took over in 2006 we have had Kopitar(19), Bernier(19), Doughty(18), Moller(19), Schenn(19), Clifford(19), JAD(19), Bjornfot(18), Kaliyev(19) and now soon to be Byfield(18) have all played in the NHL as teenagers. That list includes four guys not taken in the 1st round, that is rare for NHL teams to do.
They signed Mikey Anderson at 19 and put him in the NHL after not even a full year in the minors, they signed Turcotte a year earlier than most of his peers were signed. Kupari was brought over to NA at 19 and saw NHL action at 20.
For a team that hasn't picked a ton in the Top 10, I think the Kings have been pretty aggressive about giving shots to younger prospects who earned the shot.