Why separate beds?

No. But the film code of the time pretty much insisted on separate beds.

It was also the most popular form of birth control back then...

It was just the code and it lasted until the sixties. Remember, all 50's and early 60's TV mom and dads had twin beds when they showed their bedrooms. What makes it so funny is that Niagara Falls was a well-known honeymoon destination, and this was even noted in the film.

Look up 'the Hayes code'.

My wife and I recently went on vacation in central California to a ranch in the Sierra Nevada that had cute little duplex cabins similar to those in "Niagara". Our room had two twin beds. We encountered the same thing just a few years ago at the north rim of the Grand Canyon. It's easy enough to pay a conjugal visit just three feet away.