Billy Goat
WKR
It doesn't stiffen the spine in the same amount as cutting 3" off your arrow. I measured static spine on some shafts with and without 2.5 inches of HIT installed and they measure the same. This is because the amount of deflection is dominated by the length of the beam, which doesn't change, and most of the bending happens through the middle, not at the stiffened end, in a static spine measurement. I do believe it will stiffen the dynamic spine somewhat, but not to the same effect as cutting your arrow 3" shorter. Quantifying this is complicated. Here is my theory: At the shot, you have a forward force at the back of the arrow from the string and you have a backward force at the front of the arrow from the total mass upfront due to the acceleration (F=ma). Shifting part of this front mass back into your arrow will shift the location of this front force back slightly increasing dynamic spine. It will depend on your point weight vs HIT weight, but my ballpark guess is that having 3" of solid core would be more like having an arrow 0.5 to 1 inch shorter.
I would go along with the same thing, however I wonder if the difference is actually just the difference in length. Like you said, using 3" of insert isn't like cutting 3" of shaft off. But it might be like the difference between the two insert systems. In other words if your insert system is an inch longer than before, that's the comparable difference in shaft length. Static spine is going to remain really close to the same. It's just less "free" space within the arrow shaft for it to react. You shorten that space and it's going to react like a stiffer spine. Just like a footer. I think this is why many of these heavier inserts work without much of a spine reaction, they are taking up more shaft than usual.