I've had to ask the CMs to speed up an account deletion request before because of a user complaining about having to wait an extended period of time to have their account deleted but I've also had users just request deletion and disappear.
But part of the point of the 24 hour delay is to give them the chance to reflect and reconsider their account deletion before it happens. Suspending them in the normal sense seems like it would be complicated and, in many cases, unnecessary.
I think it'd be more helpful if there were some way to preserve the user's recent activity log on the deletion stub so that moderators can review quickly if the user has been deleting or vandalizing their posts and have easy links at hand to revert those changes if necessary.
I'm hesitant to say that all edits and deletions should be prohibited because there could be legitimate reasons to do these actions - a sort of "getting your knitting in order" before you leave. Not all users remove their accounts because they're disgruntled and wish to wreak havoc on the way out.
But I also think that part of the problem here may have been the deletion process. For users with sufficiently high reputation or votes, this is done manually, not by the system. If this user fell into that category, this seems like a check that should be done before the account is actually deleted.
Perhaps site moderators should be given an alert for any users requesting their account be deleted who would trigger manual deletion and one of them should review the account before the deletion occurs, but not immediately upon the request for deletion, to make sure that none of this is being done. If it is, they can revert and suspend the user manually to prevent additional harm before a CM actually deletes the account.
This takes some of the work off of the CM's laps - a moderator can easily perform these checks and then give the account a "ready for deletion" stamp when the account hits 24 hours.