We have seen this jutsu performed three times during OG Naruto and Shippuden.
Why the first edo tensei done by Orochimaru was considered weak? Also, he used White Zetsu for 4 hokages while it is said it needs a living sacrifice.
Kishimoto, like most mangaka, are negligent in plot holes and not even fixing them in later databook/stories. With Boruto ongoing, I don't think any more info would be provided.
From what the Naruto manga/anime has, each occurrences of Edo Tensei have differences and also due to inconsistency from what Kishimoto had in his mind in earlier arcs and later stories.
Even for the creator of Jutsu, Tobirama, we never see his usage on Edo Tensei, but it's likely the resurrected ones were not at full power and he could only controlled a small number of people(per chapter 521).
The first Edo Tensei we see in series, during Orochimaru's fight with Third Hokage, is the most limited one, as both first and second Hokages were not at full potential. It's the result from Kishimoto not fully setting up for power level of the First and Second Hokages and also intended for aging Hiruzen not to be ass whooped immediately.
If we check the kunai with talisman put into head of Edo Tensei resurrected ones, the one used in Orochimaru's Edo Tensei and Kabuto's are with different colours or scripts.
It's likely that Orochimaru has refined the control aspect of Edo Tensei over the years, before his defeat by Sasuke and later Kabuto learnt all things left by Orochimaru, including Edo Tensei and using it.
The last usage by Kabuto, he claimed there is no drawback, not even requiring to use chakra, etc. But his allowing to semi independence of target sometimes leads to losing the restricted.
So while having some drawbacks, his usage is better than Orochimaru's previous Edo Tensei.
I don't think Edo Tensei is as simple as having a body part of target, a sacrifice and the Jutsu itself. The quality of sacrifice/host matters to some level. Kabuto said to "modify" things for Madara, though we don't know exactly(maybe making Madara younger, while resurrected with same power at his time of death).
The last one used by Orochimaru, the hosts are clones of White Zetus(at this point, containing large amount of Hashirama's cells or DNA as well). Unlike other resurrections, the 4 Hokages are at full power and if not for Orochimaru switching to take over another White Zetus's clone(and thus Hashirama's cell), he could not have been able to restrain Tobirama. One distinct note for this is, during this resurrection, there is no kunai with talisman used. Also Hashirama's is still freely movable even after Orochimaru's restraining the resurrected.
So compared with other resurrection of Edo Tensei, cases of Madara, plus the last one done by Orochimaru, have different kind of host, so unless stated by Kishimoto otherwise, we can say the "quality" of host matters as well.
For the case of White Zetus being alive or not, I would like to put some light on origin of White Zetsu. White Zetsu is a part of the victims of the first Infinite Tsukuyomi, just like spiral face Zetus.
White Zetsu later merged with Hashirama's cell(either by Madara or Black Zetsu), mainly with the clone of Hashirama embedded in stem of Demonic Statue of Outer Path. The army of White Zetus is basically containing Hashirama's cell, as it's cloned/cultivated from original White Zetus, as appeared in biopsy done by Sakura and other Medical ninja, during their night raid.
This goes back to last Edo Tensei by Orochimaru. The ones put as spores like fashion on Sasuke, were brought out by Orochimaru's advice of putting in Sage/Natural energy by Jugo. I would say living clones of original White Zetsu, which is result of a cocoon of first Infinite Tsukuyomi, with consciousness, is kind of living organism, and meet requirements as host of Edo Tensei.
