I was just looking at the tallest building in Los Angeles [[which is also considered the tallest west of the Mississippi River).
https://en.wikipedia.org/wiki/Wilshire_Grand_Center
This building is actually 934 ft. tall with a 166 ft. mast, thus making it 1,100 ft. tall.
The old 800 ft. design Hudson's Tower with what looked like a bottle opener at the top would have looked out of place with a mast... but now the new 912 ft. Hudson's Tower design has a lot of set backs with a flat top, so a mast would no longer look out of place. That could easily take it to over 1,000 ft. And the top of a spire/mast/antenna is how building heights are determined these days.
When you view the downtown LA skyline... the tallest tower [[with mast) looks like the 2nd tallest [[based on top floor height), after the rounded US Bank Tower.
https://www.flickr.com/photos/hunterkerhart/35160023003
Even the new 1,776 ft. One World Trade Center in NYC is only 1,368 ft. to the roof, with a 408 ft. mast.