"Inflammation is a basic life process, not a reaction to the food you eat. Inflammation plays an active part in wound-healing. Teething in infants has an inflammatory component. Systemic inflammation is ubiquitous during and following parturition in mammals. There is inflammation everywhere, it's as generic a word as "oxidation" and "metabolism.""
Everything you have said is true.
What I think you are missing is that there is both a per-calorie inflammation cost for all food inputs and a minimum inflammatory startup cost just to metabolize at all.
More simply: 1000 calories spread across two meals will generate more inflammation than 1000 calories in a single meal.
There are two analogies that I think are useful when thinking about this:
First, introducing food inputs appears to be an interrupt for most other bodily activities - even very essential ones like sleep and reproduction, etc. You might consider how many hours each day your body spends not digesting. It doesn't take much to increase that by 50% or more...
Second, electric motors like pumps and fans have failures ("deaths") that are much more accurately predicted by number of start-stop cycles than by the number of hours run. Startup is expensive for these devices and I suspect that startup is expensive for our food metabolism as well.