Suppose you have a random number generator that produces your private key, as all serious wallet software and hardware have. In that case, you lower the entropy by including known factors such as birthdates and passport numbers.
I'm trying to understand your point, but I don't see it.
I suppose you're assuming a case similar to that of brainwallets. If so, you're mixing different concepts.
Here, the initial entropy of the seed remains the same because by encrypting, you're not modifying the original source of randomness.
Or maybe you mean that it would be easier to guess, but it is not like that, because the attacker faces several challenges:
1, Find the encrypted seed.
2 Guess that an additional layer of security was used.
3 Guess which method was used.
4 And last but not least, in an extreme case that knows all the above, he will have to brute force, at 60 million iterations per attempt, which makes it extremely demanding.