What do you mean by “human assistance”? Are you referring to artificial insemination? If so, it appears that artificial insemination is rather far from universal — the alternative being natural breeding — for example:
Almost 80% of dairy producers in North America use artificial insemination (AI) to breed cattle, compared to only 4% of beef producers. [source (archive)]
With pasture breeding, […] a bull [can] sire more than 40 calves in a 6 to 8 week calving period. [source (archive)]
[They] are susceptible to a wide variety of common diseases they only survive through our medication and care.
Sure, but this doesn’t necessarily mean that they are all certain to contract said diseases, nor is it certain that the transmission rate would be high enough for all cows to die off.
What do you mean by “human assistance”? Are you referring to artificial insemination? If so, it appears that artificial insemination is rather far from universal — the alternative being natural breeding — for example:
Sure, but this doesn’t necessarily mean that they are all certain to contract said diseases, nor is it certain that the transmission rate would be high enough for all cows to die off.