Writing made us bad at remembering. Socrates was famously a critic of writing for this reason[1]. If we can say anything about the effectiveness of the argument, it's that it's completely impotent against new technology and tools.
Not if you care about these skills! It's not like Socrates was wrong, it's just that the world moved on without him. Having a good memory has nearly zero value these days.
Otherwise the information the average person knows about the past is probably even worse, pop memes aside ("Cleopatra's nose", "Egyptians worshipped cats").
Even the immediate past - like 10-20 years before people were born, would be a foreign concept, if it weren't for the ocassional period movie and tv series reference.
You'd assume so based on the prevalence of information, but I'm not sure there's any evidence of this. Hell from my own interactions about the past with others, you might as well have completely wiped everything before WWII from cultural consciousness and pretended like the last 80 years are the only ones that matter. Some days it's feeling more like the last 40 years represent the only world people can even imagine, let alone have an opinion on.
On the other hand, thanks to the invention of writing, we have a chance at having at least some reliable knowledge about how people lived thousands of years ago, across the world. (I assume your comment is at least partially tongue in cheek. But I take your point that, just because writing gives us incredible ability to make records and to learn about the past does not mean people will use it.)