But how do you gather the diverse sources of opinion and how long does it take to do that?
Don't really understand the question. Not sure what part of the whole process you refer to.
It doesn't take very long to stroll down a few hours worth of tweets, depending on how many people you follow. I generally scroll down the list, opening potentially-interesting links in new tabs then close twitter and set about reading the links I've opened.
It's more convenient than visiting and browsing dozens of different websites.
And again, depending on who or how many people you follow you will have to filter out a certain amount of vacuous rubbish but that becomes second nature after a while.
That's just one use. There's plenty of mindless chit chat involved with my twitter use but I don't mind that and it's not mandatory.