I found a post from a few years ago with someone asking for the same thing on Stackoverflow Meta, as well as a related suggestion that replied-to comments be undeletable without consent from the repliers.
This discussion on those questions points out some significant problems with this. There are two that I think are most germane. First, it's not possible with the way comment notifications are implemented (or at least how they were implemented in 2010). Second, if a person has more than one comment, you can't tell which one a replier was replying to, since @-somebody replies to the person, not the comment. You can see some other stuff in the discussion, and if you search SO Meta you can find a few other questions that touch on similar issues.
My feeling is that the actual benefit of this feature would be rather small. The only real gain is that people can sometimes avoid "looking silly" because of a dangling comment, even though it would only ever look silly to people who aren't familiar enough with the system to realize that a previous comment was deleted, and even though it still wouldn't avoid silly-looking dangling comments that neglected to use @-notification to mark which comment they were replying to. On the flip side, it has the potential to result in a fair number of distracting notifications due to comment deletions on old threads that the replier doesn't care about cleaning up.
I'd just like to reiterate what I said in my comments: comments and notifications are not a Money SE, issue, they are a StackExchange-wide issue, so I think any solution should be considered with regard to how it would work across all StackExchange sites. Likewise, from a practical standpoint, I'm skeptical that this is going to get much traction if users on the high-traffic SE sites like StackOverflow don't see it as a major problem.