The downside is that unless its a morai, your unit needs to be level 6 (4 if morai) before you can give it vampirism. This generally takes a while and usually ends up with lots of dead units. On the other hand, you can build a vampire (strength 5 instead of strength 6 champion), and without ever having to send it into combat give it combat 1-5 or drill 1-4 or anything else that you want. This gives them a fairly great advantage in building tier 4 units, as it can get promotions from the start (most of their teir 4's start as vampires). This is considered balanced though because most people upgrade their most experienced tier 3 units to the tier 4 units, which puts them on a somewhat even footing.
With morai, this promotes spamming units like nothing else and whichever ones get to lvl 4 then get upgraded to vampires and become your city busters. With Vampires, this promotes building a large army early, then giving them upgrades over time, rather than spamming them like the end of the world is coming.
That being said, there is no reason at all to not give a unit vampirism if it can get it. But don't think that makes the vampires super OP or anything... everyone else has some sort of counter to it, and vampires are very expensive (generally cost about 1.5x the hammers of a normal unit). The easiest way to remove them from the game is to rush them early. The easiest way to lose to them is to let them grow unhindered.
-Colin