There is absolutely a need to keep all records, although there are still some limitations as to using portfolio trackers.
Your data is exposed to third parties who is technically and potentially capable of conducting data mining on all of its user data, leading to privacy concerns and potentially to give themselves a better understanding of the market (although these are just theoretically, and have not been confirmed). So if you're extremely concerned about privacy, you should probably use a spreadsheet of your own.
But all the rest of your points definitely still stand - especially come tax time, it's hard to dig back to old trades all the time. You'll appreciate then why it is crucial that you record all your trades down as you conduct them, no matter how much hassle it may seem at the time, because they will compound as you go along.