To be fair, hard drives are not necessarily more future-proof than audio cassettes. A hard drive typically lasts, what, 10 years, whereas a cassette tape is probably good for 50 years. You need to back up the digital copy onto different devices.
A single hard drive can be part of a larger fault-tolerant storage cluster, not to mention much more easily duplicated and backed up. The digitization process is key.
Once you have it digitized, making copies is trivial though. Every time you listen to a cassette the quality degrades slightly. You always run the risk of a machine eating a tape as well. Maybe the cassette will last 50 years in the box, but it won’t last 50 years of active use and you’ll want to make other copies, the earlier you make those digital masters the better.