Sometimes I wonder, as a mind experiment, how close we could get to practical carbon burial with a process based on sinking polymer blocks in the ocean: the specifics of the polymer blocks wouldn't matter at all as long as the surface doesn't degrade into spreading microplastics and total density would be high enough to sink, and they could be shaped like standard containers for easy logistics. The result of the mind experiment is always the same, even that could not possibly compete with leaving fossils underground.
Additionally, carbon capture does not necessarily mean we are burning "fossil" fuels. Carbon capture could be using the Sabatier process to create methane from the CO2 in the air, which you then use to power rocketships/jets/etc, which we are still not very close to electrifying.
Why? What is wrong with capturing carbon the way trees naturally do? (Honest question)
The closest thing we have today to those "eternal tree corpses" are peat bogs were decomposition is kind of broken even today (and guess who discovered that dried up peat can burn, even if it's a very dirty fire? Humans. We just love oxydating carbons).
https://www.sciencenewsforstudents.org/article/recycling-dea...
Though word is in the air that the previous assessments might have been very optimistic.. although that will probably only be discussed in 2022 when the 6th assessment report is to be published. Which presses the issue only further.
[0] https://www.ipcc.ch/site/assets/uploads/sites/2/2019/02/SPM3...