The expectation is that even in cases where you give them a specific archetype, they can take another one with the rest of their archetype feats afterward
While I agree with the general premise that you get free-archetype feats all the way up, and (absent a campaign-specific restriction to the contrary) they can be from any combination of archetypes (subject to the usual requirement to take two feats before the next Dedication - again unless waived), I do not think that that bit is saying what you think it is saying.
"If the group all has the same archetype or draws from a limited list, you might want to ignore the free archetype’s normal restriction of selecting a certain number of feats before taking a new archetype. That way a character can still pursue another archetype that also fits their character." (Emphasis mine.)
What it says to me is that, if you are using the variant with a specific mandated archetype in the extra slots, you might allow the PC to take a second archetype
alongside it in their normal rather than having to wait until they are three feats in.
I can see how players would like this option. Players will always say yes to more stuff. Coming from a DM angle this just feels excessive.
Not always. I personally like the idea, but the reason I have not instituted it yet in the game I am running is that I am not sure how some of my players would feel about it.
Heck, hybrids don't show a particularly dramatic impact in most cases for a long time, and that's a lot stronger and option than free archetype.
What are "hybrids"? Is that another name for Dual Class characters, or a third variant I am unaware of?
Anyway, on the subject of the OP, I am still debating whether to do it for the current campaign (we have started, but the players are still first level and the variant does not kick in until second). As I said above, I like it, but I am not sure how the players will react to needing to pick ten more feats.
I decided to wait until I saw how the PCs were getting on before making the final decision. Since we have had one PC death already, I am going to go with "not great", so I am leaning towards using it. I have pretty much come to the conclusion that picking a lot of feats is something you just have to get used to with PF2.
As to how my player would have reacted had I gone in the opposite direction, with one possible exception I doubt any of them are aware it exists, so there would have been nothing for them to react to.