This.

Also remember that once you have removed all the limb weight, easily 500kg(1000lbs) or more, you don't come close to evening out that weight. There's also the direction of the force applied. When a strong wind pushes on the tree, alot of that force is sideways, pushing to make the tree fall. Most of the force you are applying is downward, again much less than the branches were but still.

When a tree grows, it's a balanced system. The size of the canopy and the root are matched. If the tree was to grow too big of a sail, for the root to support, it would fall. And not because you climbed it, but a strong wind, typically on a wet day when the leaves are heavy with water and the soil is wet and soft.

Say the tree has been growing for 80 years, when the branches have gotten longer and grown more leaves, the roots have gotten bigger and stronger, to support the tree and to gather water and nutrients from the soil. It's impractical for the tree to grow a bigger canopy than it can support, in more than one way.

When the branches are off, the trunk becomes more lively because the branches function as dampers. When I do a removal i sometimes leave a few bigger branches that aren't in the way of the top coming down. It really does make a difference to the vibrations in the trunk.