This question repeats itself over and over. Are you American or British? Which exact connotation do you see and do you have some authoritative resources for that?
Here other native speskers say they would almost always use "can't"
Something like "Nemůžu vidět." would indeed sound very strange in Czech.
In the linked reference, British English speakers would say cannot, while American English speakers would say do not. From a member in London, "That's right, it's generally AmE 'I don't see it' but BrE 'I can't see it'."
I used the keyboard to enter "do not" and it was accepted, which is good. Would it be possible to add it to the word choices?