Practical application of Electrum's Encrypt/Decrypt message feature? It's pretty clear how signing a message with a Bitcoin key can be useful in proving ownership of funds.

However, it's far from clear how encrypting a message with a Bitcoin key can do anything useful. This feature is available from Tools/Encrypt/decrypt message, and appears to use ECIES or some variant of it:

https://en.wikipedia.org/wiki/Integrated_Encryption_Scheme

It seems that at least one developer is doubtful about the security of such schemes:

https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2014-August/006581.html

Security aside, what practical reason would anyone have to encrypt a message with a Bitcoin key?
Presumably, using a bitcoin public key you could encrypt a message, and only the person who controlled a private key associated with that bitcoin address would be able to read the message.

It's really a question whether you have confidential/private/secret information that you wish to share.

If you're looking for an hypothetical use case, imagine you paid your doctor in cryptocurrency for an embarrassing medical test, the result could be sent back encrypted such that only the person who paid can read it.

Or, Lets say you paid for software license online with cryptocurrency, the software key can be sent back encrypted such that only the person who paid could read the key.