I'm not sure I understand, what's the problem with following people and using the timeline (maybe even in a third party client that sorts it chronologically)? What do you gain by only navigating to profiles manually?
The timeline is controlled via algorithm, and either filters or selects things to show you based on an uncontrollable process which is likely just meant to make you more outraged, annoyed, etc. to keep you engaged with the platform. Not only is that unhealthy, but it doesn’t make for an enjoyable experience almost by definition.
Can't you just set the timeline to show latest tweets first to avoid this? The alternative is certainly terrible (though mostly because it hides a bunch of tweets I actually wanted to view rather than because of any outrage), but the option to disable it is there.