Due to the nature of how marketing email engagements are logged to the contact timeline, the body is not read in the same format that sales email activities would be. Due to this, we are unable to sync the marketing email body in the task activities.
It would take time since you have to do it for each marketing email, but it is an option.
Finally, I did find this idea that is touching on a similar feature request that I'd recommend commenting on your use case and up-voting. We use our Ideas Forum to collect suggestions/feedback on how we can improve the product for our customers. The product team pays particular attention to the top-voted ideas.