Why does Zz'rot not work?

Right now Zz'rot is one of the most cost efficient items in the game, gives double resistances and enables splitpushing for tanks. At least that is what it is supposed to do. By playing it myself lately because it got buffed I discovered a big problem with it which may just be the reason why it's not good.

Normally when you're splitpushing you create a hard decision for the enemy to make, either they send a lot of people to stop you or they pick fights and objectives elsewhere. That means that when you are splitpushing you have to retreat very often and when people come to catch you just to go back to tower pushing when they gave up. When they stay the have less members in the teamfight that is going on elsewhere, which is the whole point of this tactic.

So while ZZ'rot gives you decent extra damage to minion waves and extremely good damage against towers if you stack a lot of HP, it cannot retreat with you. Imagine the following scenario: You are at the Inhib tower and want to get it down by splitpushing, yet the enemy team send two of their own to stop you. In the meanwhile the rest of your team is sieging the second tier mid tower.

A Jax could easiliy ward hop and retreat since he has warded everything and then come back to finish the job because they have to send people back to deal with the mid sieging. A Singed with Zz'rot on the other hand will not really have this opportunity since when he retreated, the enemy found and destroyed his ZZ'rot. With it being gone he has little to no DMG to finish off Towers since he can now only bop it down. Tl:dr: The Zz'rot is way too easy to find and destroy and so your splitpushing capability is very easy to shut down this way.

My take on fixing this problem would be to make it so that you are able to pick it up after you put it down. If we come back to the scenario above, Singed could've just taken the thing and reset it's cooldown by a fair amount by picking it up when he was running away from the enemy team. By the time the two team members went back to deal with mid he could've just put it up again and finished off the tower and maybe even an Inhib.

I'd really love this change to go live since a lot of tanks do have everything they'd need to be a great splitpusher except for damage on towers. An updated Zz'rot like that may even be able to push a lot of tanks that are kinda unviable now back into the meta, Singed being the big one.