Zyra is an AoE focused mage who excels in teamfights, and her plants need to be in the middle of the chaos to do their thing, specifically the melee plants. Giving them enough health to be able to get a hit in in the middle of a bunch of aoe would be very, very tanky for nigh spammable minions, and making only the melee plants have different health would make it unintuitive, so they went with ward-style health. Iirc, on realease (or PBE at least) Zyra's plants did have normal health, and they just got deleted by a passing sunfires.
Shaco's boxes should have a high risk to get a great effect. Getting a 5-man fear from a box should be really difficult, whereas a zyra plant will get a few hits off for some damage at best.
As for Heimy, the vulnerability from AoE damage is a trade-off for duration.