they are both valid ways to make a game imo, like its obvious that Gordon isn't the Protagonist as much as a Plot Device and Cameraman for the other actually developed characters, but thats like an ok way to tell a story. its the same with call of duty campaigns for example (imperialist though they may be), you are mostly there to see the Cool Named Characters do Awesome Scripted Animations. FPS games still basically control as if you are a wheeled boxy drone with a gun attached, so until they can make the Awesome Scripted Animations an actual real-time gameplay feature, it makes sense to go the Player As Secondary Protag/Cameraman route - since you can't do the Cool Scripted Animated Takedowns that Captain Price does, due to the limitations of FPS controls, they just make you watch other people do it.
in terms of self-insert i think voiced protagonists with voiceover options are better, a silent protagonist means that any voiced input of your own that you might 'self-insert' into the silence goes entirely ignored and unremarked on (the NPCs will never respond to your DIY 'freeman's mind' act), the silent protagonist kind of relegates you to a passive observer in terms of character interaction. not that this makes the silent protag 'bad' but i don't think the reason it can be good is because of self-insert/freedom of choice. an exception is if there are dialogue choices for the silent protagonist, but then the writing chooses your tone and you might as well have a set of voiceovers to choose from.
they are both valid ways to make a game imo, like its obvious that Gordon isn't the Protagonist as much as a Plot Device and Cameraman for the other actually developed characters, but thats like an ok way to tell a story. its the same with call of duty campaigns for example (imperialist though they may be), you are mostly there to see the Cool Named Characters do Awesome Scripted Animations. FPS games still basically control as if you are a wheeled boxy drone with a gun attached, so until they can make the Awesome Scripted Animations an actual real-time gameplay feature, it makes sense to go the Player As Secondary Protag/Cameraman route - since you can't do the Cool Scripted Animated Takedowns that Captain Price does, due to the limitations of FPS controls, they just make you watch other people do it.
in terms of self-insert i think voiced protagonists with voiceover options are better, a silent protagonist means that any voiced input of your own that you might 'self-insert' into the silence goes entirely ignored and unremarked on (the NPCs will never respond to your DIY 'freeman's mind' act), the silent protagonist kind of relegates you to a passive observer in terms of character interaction. not that this makes the silent protag 'bad' but i don't think the reason it can be good is because of self-insert/freedom of choice. an exception is if there are dialogue choices for the silent protagonist, but then the writing chooses your tone and you might as well have a set of voiceovers to choose from.