You'd think they'd want more human-looking troops, as opposed to less human ones, considering the PR campaign they're trying to run.
The idea is that the aliens came and solved all of our problems because man is stupid and all that. If the aliens turned themselves to look more like us that would kinda actually have the opposite effect. It would be like if a god came down and told you that all your problems are due to what you are but he'll help you anyways, then turned around and made himself just like you were before he was there. It directly conflicts with the whole "because humans were stupid" thing.
On the other hand making yourself look more alien actually amplifies how much different you are than humans, and lets everyone identify you as a "glorious savior" on sight.
But no, they do have a militarized humanoid police force the populace can more easily identify with, and that's ADVENT. The aliens were the saviors, but their PR speech wouldn't really claim "man is stupid" if they want to appeal to humans as opposed to alienate them (pardon the pun). The real aliens remain mostly behind the scenes, while ADVENT appears to be the face of the new world order. A softer way of portraying global subjugation.
To a point, however, as ADVENT troopers bleed yellow, meaning there's likely hybrids at least beneath the full body armour, and the organization's spokesman looks suspiciously like a Thin Man.
As for aliens and Earth diseases, a) for them to be affected first they'd need to have a compatible biological structure (otherwise it's as ridiculous as the computer virus from Independence Day), and b) you'd think aliens so advanced and well-versed in genetic engineering and splicing would remember something as basic as "coding" an immune system suitable for the planet in question.
Additionally, I believe people flock to the advanced, alien-run cities precisely because of benefits like advanced healthcare and the like, so it's easy to conclude the so-called Benefactors have triumphed over Terran diseases.