Trees work, but take a long long time to grow.

Trees are good but are largely a temporary store. Most of the carbon they capture ends up be re-released upon decay. Of course some does get more permanently sequestered in the ground, but a relatively small amount, and is a very slow process. I'm all for planting more trees, but I'm afraid the problem can't be entirely solved by merely planting more trees. It's also a rate problem - it may not be possible to plant enough trees to completely offset the rates we're adding carbon to the atmosphere.

A tree normally is carbon-neutral. Is captures carbon when it grows then releases it when it dies and rots.

Unless you have an ecosystem that prevents rotting (e.g. an anaerobic swamp) in which case you have steady accumulation of carbon (e.g. in a form of peat, which is a fire hazard btw). When people speak of planting trees to capture carbon they rarely mean creating swamps.