The main benefit - IMO - is that it's relatively compact, lightweight, and solid compared to CO2. If there was a cheap and simple way to condense CO2 into a solid, we could stuff that into the ground instead. But CO2 would have to be stored indefinitely - we will probably see the catastrophic effects of what happens when stored CO2 is released in the atmosphere (permafrost, ice and ocean sediments are releasing their stored CO2 atm). Actually, fossil fuels can be considered to be stored, solid or liquid CO2 already, accumulated over tens or hundreds of millions of years.

On that scale, putting something away for 10K years seems relatively trivial and safe compared to CO2.