I think, yes and no. I don't think that current Western methods literally replace traditional kappô. The answer is more nuanced. Firstly, one may not compare methods that can be applied in a modern emergency room or operating theater with kappô. The first options after all are the exclusive terrain of trained anesthesiologists and emergency physicians and are not present on the spot where jûdô activity is conducted. Kappô were intended for every qualified senior jûdôka to be applied on any occasions.
It is also not completely true that Western medicine offers ready manual strategies that can cope better with all of the indications for which kappô exist; some yes, others not. When it does, it is not so much because the intervention itself is better, but because our understanding of physiology evidently is much better than in the 1630s when these kappô first were brought to Japan. For example, we now know that the most important thing is circulation and we now know that if the brain is deprived of oxygen for more than 4 minutes during normal atmospheric and adiabatic conditions that irreversible damage occurs. But we know that breathing is secondary to circulation, and we know that a person who isn't breathing is not necessary dead and can have a pulse although eventually circulation will cease. We know that a when a person isn't breathing for some time aht acidosis will occur due to accumulation of carbon dioxide that may require buffering by bicarbonates, etc. With this information trained physicians can more adquately address some problems, but again, one may not compare trained physicians with standard jûdôka since the kappô were also meant for standard jûdôka.
Nevertheless, from this information we know that when a person is suffering from acute drowning symptoms that it may not be sufficient to simply lie him with his belly upon a person in yotsunbai, but that circulation and breathing require most attention. However, that does not mean that the kappô approach has no use, since IF the person indeed has water in his lungs, this needs to be evacuated in order to induce independent breathing, and apart from mechanically causing that evacuation either or both by mechanical pressure or gravity there really aren't any other ways to do so, since you don't really carry a medical pump with you.
Similarly, what approaches does modern medicine have that on the sport can be applied to epistaxis (nose bleed) ? You can apply cotton balls into your nose and apply manual pressure, but apart from that if it doesn't stop ? Sure, there exists cotton drenched in epinephrine, but the average jûdôka does not have that with him on the tatami. I know from personal experience that reflex kappô therapy for nose bleed has stopped gushing nose bleeds that everyone else including the paramedics failed to stop.
So, in other words, I think that it is more our current day knowledge than an exact replacement of the plethora of kappô techniques that is in order. Many kappô focus on breathing rather than on circulation, which could be a problem since for some reason it seems not to have been fully understood in those days that breathing is secondary to proper circulation. You cant induce breathing in a person that doesn't have circulation. We also know that not having a pulse can be caused by several things of which some are more serious than others, and various require a different strategy. Absence of a pulse could be due to severe drop in blood pressure, but it also could be due to fibrillation or asystole. All three require a different approach, but no effective approach exists without access to modern medical equipment and drugs, and even differentiating between the three in terms of diagnosis maybe hard or even impossible without modern diagnostic apparatus. Asystole even has a poor prognosis with modern medical approaches. So in that case one can't blame kappô since even a qualified medical doctor will face a near impossible situation to diagnose and address any of these conditions when outside a hospital deprived of modern medical diagnostic and treatment facilities.
Doug talked about "martial injuries occurring on the tatami", but not all serious things that occur on the tatami are really "martial arts injuries". This is particularly so with some fatalities such as a rupture of a major cardiac artery. These can be incidences that only in a unique circumstances such as when they occur in an emergency room or operating theater have a chance for survival and are in all other instances fatal. For that reason one can't fairly include all medical indications when considering kappô.