I think everyone has his own motivations.
I for instance can't remember a single name on any system "first discovered" tag, not even from the most popular/famous systems. And even though I sometimes see the names on the system map, 30 seconds later I already forgot. I can't even remember (nor do I care to be honest) a single system where I was the one to "plant the flag".
So from my own personal point of view, first discovery tags are rather pointless, unlike the guy who climbed Everest first (which I only learn about from your post, and most likely have forgotten about in an hour

), I doubt anyone actually notices the names on the tags, and still remembers them after a few minutes.
The reasons I explore in the game are the same reasons why I want (and some cases already did) to climb to the summit of Mount Teide, Mount Vesuvius, Mount Stromboli, Mount Tambora, Mount Nyiragongo (especially this one, probably next fall if nothing wrong happens meanwhile), Mount Masaya, Mount Yasur, Mount Marum, etc. To see the wondrous sights and stare in awe, humbled by the sheer raw power of Nature's mightiest creations, see them and feel them with my own eyes and senses. The fact many others were there before won't matter one yota when I'm on top of Nyiragongo's 3500meter summit, staring in equally high doses of both fear and wonder at it's 2km wide, 770m dead drop caldera and it's huge, oozling, glowing, almost hipnotic lava lake.
I explore in ED to see the
Nyiragongo's out there, to experience the galaxy's most wondrous locations (or die trying), to see the biggest mountains, the deepest canyons, the planets closets to the stars, etc etc. Who got there first matters jack to me, as long as I can go there as well. Landing at Betelgeuse 2 or Hades Edge 1 and see the monstrous, gargantuan sunrises didn't feel any less exciting just because someone else (whose name I will never remember) got there first.
As for ED's planets, while most do actually look all the same (especially since the topography nerf which came with
the beigening), there are still always a small fraction of them who are different, and those are the ones worth finding.
But this is me, to each his own

My way is neither better nor worse than someone else's way.