"while still being really tanky"

Vladimir is really only as tanky as he builds with the added use of Sanguine pool.

Transfusion healing is pretty underwhelming except when empowered, and even then just how much AP do you generally reach in a match? 300 at best? Comes out to 17% of missing health plus a base amount up to flat 200 points. Whoop dee do. Darius gets 12% of missing health per champion hit with his Q on a cooldown mirroring transfuse (up to 36% which transfuse will never match). It does it every use every time; no waiting 2 hits to get the good heals. And I'm sure you've seen plenty of 3-4 item fiora's recover well over half their health when their ult heal aoe triggers.

Maybe you're trying to say sanguine pool adds a lot of healing? I dont see it. It doesn't do that much damage. From 20-75 per second with 2.5% of bonus health. Supposing you didn't get abused for playing Vlad lets say you manage to get a rylais, haunting guise, and spirit visage by the 25 minute mark with 200 health from runes. Your sanguine pool has an extra 30 damage; if you skilled as most vlads do its still rank one for a whopping 50 per second and 15% of that as healing is a lower rate of health recovery on a single target than a health potion.

Where is this great iconic healing?

As discussed Karma can get a massive heal off empowered W based on her max-health-not-missing-health and regular shields that take into account armor/mr. The only thing stopping mid-karma or top karma from being as or more tanky than any vladimir is building tanky, which is a valid choice.

I might be underselling Sanguine Pool somewhat, sure. I'll concede that. And having it available; mediocre stats & long cooldowns aside; does give vladimir the slipperiness needed to get past the frontline... once. But that really isn't going to happen without someone elses initiation and he certainly doesn't have the dive potential of an assassin. Furthermore Vladimir builds don't fair well or make it to 25 minutes building full AP; so I really think any comparison in late game damage that claims vladimir is going to become some damage powerhouse carry is extremely generous.