Perhaps the Spanish were late at recognising the direct causality. But there is sufficient documentation that US troops gave blankets from infected people (smallpox, etc.) to Native Americans and that they would become ill.
Certainly we should not believe that the Spanish were less observant or intelligent than the Anglo-Saxons. It would be sufficient that the conditions under which indigenous Americans were forced to live denied them even the chance of resisting the illnesses Europeans brought with them. Deliberate neglect, refusal to treat their lives as of equal value and therefore deserving of the best possible care-- these are the factors which aggravate the infection of America by the Spanish, Portugueses, English et. al.
They may not have had the wonderful theory of Lawrence Summers for defining the relative worth of people exposed to toxic waste but they certainly had the experience to say that slave labour was cheap. In Europe it took the Great Plagues and the sheer scarcity of people to pursuade the ruling classes that labour had to be paid properly-- because there was not enough to go around. "Discovering America" was not only about finding precious metals but about finding what at least one scholar called "red gold"-- indigenous slave labour.
However, it is no accident that "reform" came after the decimation. African slavery was not only promoted because of climate or the "inability" to enslave the indigenous, it was also because the indigenous population was exhausted and the supply was inadequate to meet colonial demand for free labour. The Jesuits were expelled largely because the "paid" better for their labour than the rest-- not because they were less willing to exploit them.
From the view of colonial economics the Spanish have been great failures, except at plunder. One could say that the Spanish "dark ages" from 1936 to 1975 are a reprise of that monumental step into barbarism called affectionately the "Reconquista". The same spirit that made Spain one Catholic kingdom was that which was borne to America. If the colonisers had not had the least notion of health and hygiene, then they could thank Mother Church for this. One is ever too fond of the cross brought to foreign lands while forgetting that a cross is inconceivable without the nails.