The heart pumps the blood to supply tissues and kidney always filters the blood to remove urea,extra water and etc. And all these are vital,so the kidney is as important as heart: and my question is: Why is heart failure treated as more critical than kidney failure?
I don't know that one is treated as more critical than the other. Both are potentially life-threatening conditions.
One in five people over 40 will develop heart failure (HF). That makes it a very common disease of aging, and as more people survive other events (e.g. MI), it will continue to be prevalent, if not to rise.
When a patient presents with heart failure (HF), whether it is to a PCP, an urgent care center, or the ER, it is treated.
In the US, the prevalence of CKD (chronic kidney disease) in people ages 60 and older approximately the same as of congestive heart failure (CHF): 18.8 to 24.5 percent. Between 1980 and 2009, the prevalent rate for end-stage renal disease (ESRD) increased nearly 600 percent, from 290 to 1,738 cases per million.
When a patient presents with renal failure (RF), whether it is to a PCP, an urgent care center, or the ER, it is treated.
That makes both conditions much more common (and less emergent) in presentation than, say, anaphylaxis (life-threatening allergies). Known rates or cases of anaphylaxis were 0.0004% for food (e.g. peanuts), 0.7% to 10% for penicillin, 0.22% to 1% for radiocontrast media, and 0.5% to 5% after insect stings.
Emergencies are emergencies, and are triaged for care based on risk, with standardized acuity scales that have five levels (e.g., 1- resuscitation, 2- emergent, 3- urgent, 4- less urgent, 5- nonurgent). To claim that one is treated as more emergent than another, one would need to present evidence that, e.g. HF is rated as emergent more often than RF.
 Lifetime risk for developing congestive heart failure: the Framingham Heart Study
 Chronic Heart Failure: Contemporary Diagnosis and Management
 Kidney Disease Statistics for the United States
 Anaphylaxis in the United States
Considering the 1999 US population of 272 million, the population at risk for anaphylaxis from food is 1099, from penicillin is 1.9 million to 27.2 million, from radiocontrast media is 22 000 to 100 000, from latex is 220, and from insect stings is 1.36 million to 13.6 million. These calculations yield a total of 3.29 million to 40.9 million individuals at risk of anaphylaxis.
 Emergency Severity Index (ESI): A Triage Tool for Emergency Department