I recommend the book Supplying War, by Martin Van Creveld. It is on the official reading list for United States military officers, and covers the history of military logistics, mostly in Europe, from the Napoleonic Era through WWII.

The insight most relevant to the question is that until WW1, most armies essentially did leave each soldier to look after themselves. This method of supplying the army is called 'forage' which means that the army spreads out and acquires supplies through whatever means (sometimes commerce, often plunder and rapine). In WWI this changed, for two reasons according to Van Creveld:

• The equipment was sufficiently different between the belligerents that they couldn't just pick it up and use it anymore. In the Revolutionary War and the Napoleonic Wars, you could just take the enemy cannon, turn them around, and bring them to the next battle. But by WWI the guns all used different ammunition, different powder strengths, and required at least a modicum of training to operate effectively.
• Highly developed rail systems finally allowed enough bulk transport to actually meet the needs of the army. Previous attempts at overland logistical support had all been failures: every army in European history depended more on forage than they did on overland supply trains, until WWI. Example: Napoleon's invasion of Russia is widely known to have overextended the French supply lines, and the Russians deployed 'scorched earth' tactics (which means to burn your own stuff so the enemy cannot have it) resulting in the defeat of the invasion. This is wrong: the French supply lines were never a significant factor, and further the scorched earth tactics did not succeed; the French army was able to get a satisfactory amount of forage from the Russian country side regardless. The casualties came during the retreat over already-foraged land; it was the cold that killed them.

So during and after WWI, a military needs to make sure it has enough stuff, that it can use, so that it can continue to prosecute the war. This cannot be accomplished by every soldier looking after themselves; they will run out of ammunition, cannot fix their broken weapons or vehicles; etc.

However, it is absolutely possible for there to be too much central planning, and this problem is centuries old. Covered in the book is the case of Operation Overlord, the legendary assault on the western shores of Europe to invade the Third Reich. It is a tale of horror, and of heroic courage; the moment in the popular mind when the war turned and the Allies effectively ensured final victory. It was also a logistical catastrophe. Unprecedented efforts went into the planning of assault, down to exactly how many cans of gas were required for each jeep, which is precisely where they went wrong. In the chaos of the invasion, whole armies landed miles away from where they were expected; armies landing nearer supply depots meant for different armies used them as a matter of necessity. The Allies did not succeed in their objectives the first day; in places ammunition ran short and vehicles ran out of fuel. The invasion nearly failed. Fortunately recovery was swift; 160,000 men were in the assault in June; 2,000,000 were in Europe by August, on the strength of a tenuous foothold the first day.

Cycling back to the initial question, how many people die in war as a consequence of logistics vs. enemy action: almost all. The largest killer of soldiers across history by far is disease; typhoid, dysentery, malaria, etc. The lack of sufficient food and shelter increases vulnerability to disease; the lack of good hygiene guarantees disease; the lack of good medical care increases the fatalities from disease. All of these are logistical questions. Since the health and equipment of soldiers has a huge impact on whether they win engagements, logistics remains a large factor in how many deaths result from enemy action, as well.