I agree with your assertion that AI will seamlessly integrate into existing software and services but my expectation is that it will be unequivocally superior as a 3rd party integration[0]. People will get to know 'their AI' and vice versa. Why would I want Bard to recommend me a funny YouTube clip when my neutral assistant[1] has a far better understanding of my sense of humor? Bard can only ever learn from the context of interaction with google services -- something independent can pull from a larger variety of sources supersetting a locked system.
Nevermind more specialized tools that don't have the resources to develop their own competent AI - google might pull it off but adobe won't, and millions Saas and small programs won't even try. As another example, how could an Adobe AI ever have a better interpretation of 'Paint a pretty sunset in the style of Picasso' than a model which can access my photos, wallpapers, location, vacations, etc?
[0]Much how smart phones seamlessly integrate with automobiles via CarPlay and not GM-play. Once AI can use a mouse, if a person can integrate with a service an AI can do so on their behalf.
[1]Mind it's entirely possible it will be Apple or MSFT providing said 'neutral' AI.