This is really interesting and many of the comments here go into the utility of this, however, verify that you aren't recording somebody else without their consent, in many places it is illegal to record to conversations without the other party's consent.
I only ran across this problem years ago when, due to a serious potential workplace issue I suggested somebody basically "wear a wire" and record their workday to catch some HR problems. We found out that the state this was occurring in had a two-party consent law and violating it was not a great idea.
This "be careful of recording" line is harmful, because folks tend to read it and assume that it is universal - there are places where it is unilaterally allowed if you have good reason to suspect not having things recorded will result in your rights being abused. Then there are places that just don't care if you do.
There are many examples, for example in the state of Pennsylvania, all parties must consent. While it is a felony to record and then playback without consent (you are correct in this case), it is a punishable misdemeanor to violate privacy (broadcasting is not required) with a fine of up to $5000 in the first violation and 2 years of prison and/or up to a $5000 fine after the first violation.
I only ran across this problem years ago when, due to a serious potential workplace issue I suggested somebody basically "wear a wire" and record their workday to catch some HR problems. We found out that the state this was occurring in had a two-party consent law and violating it was not a great idea.