The idea is based in the hypothesis that old trees grow slower, because the general universal rule that mature species spend resources on sexual reproduction, so they have less resources to grow

This is just a general rule, but the real life has a few caveats.

1) Grow is complex.

The first problem is that we don't really know "how much" slower is "slower". Has not being studied for most species, because finding a 500 year old ash that is not pruned or coppiced is basically impossible [1].

And we need to remind that trees are clonal organisms arranged around a very few parts that repeat themselves. Even if old trees would really grow much slower than saplings, they have a huge, huge difference on the --number of growing points--. This should overcome any speed difference. The result is that older trees still add mass on a velocity that young trees can't.

Other problem is that identifying grow with "how taller respect to the last year" is not practical. Biomass is the correct term in ecology. Young trees grow abnormally fast because they are searching for light. And this fast grow is the thinnest possible that can support the tree and still put it over its competitors. It can't be sustained later without risking for the tree integrity. This grow shouldn't be promoted. Wider is what we want. A tree is not growing slow just because is only 1cm taller than the last year. Mature trees have a "deploying umbrella" phase.

2) In the real life, trees often don't grow a lot the first years.

Most of the big oaks (and I had cultured a few) show a frozen grow in the first two years. They use it first year to make a deep root and 2 (two!) small leaves. Period. In the second year maybe four to eight leaves if the area is very favourable. The whole oak weights... dunno, maybe 50 grams? at this period. The CO2 captured from the air is close to zero and even could be a negative value while the sapling feeds on its acorn. Then at the fourth year there is a phase of (maybe) fast grow for a couple decades, but only if there aren't herbivores around and only if the area does not receive light.

In the same time, older trees would have included tens or thousands kilograms in each one of its main branches and the same for their main roots. Plus the soil generated. Plus the fruits.

And we can save the best for the last. Mature trees produce pollen. This is an output in our supposedly Carbon neutral system.

The number of people that had quantified seriously how much pollen produces a tree could fit maybe in a small room, but I'll assume that a fair sized tree produces tens of Kg of pollen each flowering season. What we know is that one single conifer can "paint" a car with pollen in no time, and can do it for weeks.

This pollen is protected and enclosed in a hard cage of Sporepollenin.

Sporepollenin is simply one of the most durable organic substances known by us. This structure is able to trap C for hundreds of millions of years in favourable conditions. Hundreds of millions!. Is --exactly-- the stuff what we crave for, and that we are looking for like crazy.

Except because some people can't avoid the itch to burn the soil. Though luck.

[1] When you coppice a tree, you modify the speed of regrow. My bet is that when on panic mode, old trees could easily have bursts of superfast grow. Easily much faster than a sapling. This mechanism is behind the recent fever (ehum, scam) of planting kiri trees.