Q/ why do you 'need' to sing this
Q/ why does it have to sound like a copy of the original
A/ because, alas, I do not have a female soprano friend who would always follow me around and sing whenever I play guitar
A/ because it sounds cool, it creates dynamics when the song begins slower/lower/quieter and then builds up.
A wounded cow

I have a (dis)advantage, compared to other newbies, of being able to hear whether the notes sung are in the chord or not, probably because I've been always tuning my guitar to itself with a pitch fork as a reference instead of just using a tuner. So when I start singing like a wounded cow, which I surely do, I just shut up and post a question here

I tried singing Common People in the same octave yesterday. It surely sounds better than when I tried to reach that G4, but it sounds... different. On the upside, I get this cool vibration in my head from when you sing in harmony with the guitar and actually hit the notes.
It's a good advice, thank you, I'll think about it.
P.S.: if you want to mock yourself a little, either record yourself singing or hold a plastic folder / sheet of paper / your hands
before your ears when you sing, as deflectors. For a reason beyond me, this will cause you to hear the sound of your voice transmitted through the air only, and not the sound of your voice vibrating in your skull. That's how others hear you. Chances are, you won't find your voice very similar to the voice of Jonny Cash, maybe teenage Jonny Cash

Give it a try, it's funny (and sad).