There’s a similar problem in physics - schools still teach Newton’s laws, even though they are wrong - because they are a sufficient approximation for many uses.
The problem is of course when people assume what they’ve learnt at that early level is sufficient to work with at a level that is above their knowledge - but I’m not sure what the solution to that is.
You can teach people Newton's mechanics and say "this is a good approximation with a marginal error for most everyday examples, the correct way of calculating it involves very complex things."
I feel the example I quoted regarding signatures is something that's not really a useful information anyway. That the RSA function works both ways for signatures and encryption is more of a fluke and not really someting you need to tell people when you explain the basics of public key crypto.
In the abstract 'encrypt with the private key' is a totally meaningless sentence for assymetric encryption. The entire point of a public key is decryption not encryption.
I do however believe that textbook RSA signing is secure in the simplest model. It is incredibly malleable but (especially when modeling the hash as a PRF) prevents forged signatures. In that sense I'd equate calling it secure to newtonian mechanics without friction and with perfect elasticity. That is, it forms a simple teaching model, and can inform an intuition on how things work. However, no-one should build things based on the model and expect it to come out correctly.
For most of other asymetric algorithms the primitive operation is DH-style key agreement function and the derived encryption and signature constructs are significantly more involved and in fact there isn't that much of an symetry between them. (and also the plain asymetric encryption operation gets somewhat pointless)