Right, but level 16 is a long way away from any time you'd consider starting to build Soul Ring. It's far more interesting when he's still just in the single digits and has enough mana to pull off one stun and then reincarnate (or, even earlier, one stun and then wait 10 seconds for his mana to regen to the point where he can reincarnate). And since this is still laning phase, having just that teensy bit of extra health regen is also nice to have, since it still makes a difference. And this is when if he gets his "free mana" from reincarnating, it's a whole 260 seconds of downtime and being vulnerable.
Also, SK can't even reincarnate off of manaboots without getting burned. It doesn't provide as much mana as soul ring does (also, notably, it does so on a much longer cooldown than the ring).
You'll want to keep a base mana buffer for your reincarnation, but you can use Soul Ring to get off that one last nuke/stun without touching your emergency reserve. Using SR to give you reincarnate mana is a bad idea because you can get stunned and then killed before you can activate it... But again, it does allow for an extra slam without going into your reserve. And early on? The difference between one nuke/stun/slow and two nukes/stuns/slows is rather significant.
EDIT: Dagon stories? Yeah, I got one. It was a private bot match, though. Dagon + Refresher on Lina.