What is also interesting, is that minikeys also has some kind of verification if input (the text found on physical item) is correct.
Yes it does but is it really useful?
Verification is based on fact, that not each combination of characters could be treated as a valid minikey - only when "extended" minikey produces hash which starts with "00" in hex.
If someone wrote down their minikey wrong is it going to be easy for them to correct the error just knowing that the extended minikey doesn't start with "00" ? I doubt it.
If anything I would kind of tend to the belief that restricting extended minikeys to start with 00 just reduces the security level by a factor of 256...but as you seem to want to imply through your calculations, it's still secure enough.
Any error detection is better than none. A 22-character mini-key has 115 bits of entropy, which is pretty secure.