Why is he considered healthy? Heimerdinger is a burst mage / control mage / siege mage that just so happens to fulfill the entire list of "unhealthy gameplay" criteria that other champions have been gutted / reworked for in the past. He is not fun to play against, and he is not fun to play as.
1: Non-interactive laning phase.
Heimerdinger puts down his AUTOPILOT turrets, up to three of them, that automatically invalidates 90% of the champions in the game. Not only do these turrets provide FREE waveclear, they have NO downtime whatsoever and easily outranges even the majority of the marksmen in the game.
2: Counterplay? What counterplay?
There is no clear counterplay for Heimerdinger.
* Take down his turrets? He will freely spam his spells on you and basic attack you until you die.
* Attack him while his cooldowns are up? Hah, not only are these cooldowns inherently extremely low, his turrets will also deal more damage than the entire rest of his team combined. Try again.
* Poke his turrets down from a safe distance? Chances are you will have to use multiple spells or the same spell multiple times to kill even one of his turrets. By the time you manage to whittle it down, he has another one ready. You will also have to give up using your spells on minions to do this.
* Farm safely under tower? He will happily poke you down even behind your tower. His spells not only outrange the tower, but also have a travel time that allows him to step under it, cast his spell and then back off before the tower has time to react. His basic attacks suffer the same issue - they travel so slowly he can repeatedly basic attack you under your tower without the tower retaliating.
* Wait for your jungler to gank? Even if your jungler ganks at the very beginning of the game, BEFORE you are put behind, they will encounter the exact same issues you do. Numbers do not help much here - the autopilot turrets that fire at an extremely fast rate can easily even the odds.
Now this MIGHT be tolerable if he fell off later in the game, similar to champions like Pantheon.
But Heimerdinger ONLY GETS STRONGER the longer the match lasts.
Lategame hypercarry that can easily delete tanks with half a combo, that can ALSO split push, tank towers and go so far as take down towers WITHOUT MINIONS.
The champion has no distinct weaknesses. It's literally just "put him behind". On even ground there are extremely few champions that can deal with him, and none that can go even in the early game.
A champion's counterplay should NEVER be "the mistakes of the player".
Now why isn't this champion popular, when he easily tops the damage, cs and siege damage charts across the boards even when behind?
Its simple: he's not fun. There's no real skill expression because half his kit is on auto-pilot. The champion practically plays itself - which means when you succeed with him, it does not feel like that much of a success because you know half the work was done by the AI in the kit itself. Add the fact that you don't really interact with other players - all you do is push a lane and keep them away from your turrets - and you might as well have been spectating a coop vs ai game. There's very little actual fighting or dueling going on. Due to low cooldowns there's also extremely little decisionmaking - using your ult is almost NEVER the wrong decision, because it'll be up again in less than a minute. You feel like you dont get to show what you're good for because there are simply no champions capable of fighting you - and it's not because you are a strong player.