the rules on Quicken say “When you cast a spell that has a casting time of 1 action, you can spend 2 sorcery points to change the casting time to 1 bonus action for this casting”. Since the casting time no longer is action, the Magic action is no longer required, instead the Sorcerer needs to use a Bonus action for it.
That is perfectly aligned with the casting rules I have quoted repeatedly “Most spells require the Magic action to cast, but some spells require a Bonus Action, a Reaction, or 1 minute or more. A spell’s Casting Time entry specifies which of those is required.”
Casting time = action: requires the Magic action
Casting time = bonus action: requires a Bonus Action
This is the same as Ready a Spell. When you Ready a spell you use the Ready action to do it, as per the description of the Ready action.
Also what about an Eldritch Knight that uses an attack action to cast Hold Person? It doesn't say in there "it changes the casting time".
There are specific rules that allow you to cast these spells without using a Magic action.