Sorry but I really can't agree with you. Maybe it is generational (I am nearly 80 so have been speaking English for quite a long time) but I would not hesitate to use it in response to the question "Do you like cheese?" "No I can't bear it!". Absolutely normal use.
However I do agree with the reverse of that - you probably would not say "I can't stand to watch" or indeed "I can't stand to go there again.." For the last example you quote I think either would be okay.
It appears there were times when it was quite common https://books.google.com/ngrams/graph?content=cannot+bear+milk%2Ccannot+stand+milk%2C+hate+milk&year_start=1800&year_end=2000&corpus=15&smoothing=3&share=&direct_url=t1%3B%2Ccan%20not%20bear%20milk%3B%2Cc0%3B.t1%3B%2Ccan%20not%20stand%20milk%3B%2Cc0%3B.t1%3B%2Chate%20milk%3B%2Cc0