Yes, immortality would be imprisonment. An eternity in this existence with no escape.
It's also the ultimate equalizer. Everyone is born, everyone dies. There's no amount of wealth, luck, work, or misfortune that happens in life that changes this. We all end up as dust.
And it goes beyond humans: everything that arises must cease.
This is one of the three foundations of existential intelligence (or wisdom).
[dead]
This was the point at which he conceived his purpose, the thing which would drive him on, and which, as far as he could see, would drive him on forever. It was this. He would insult the Universe. That is, he would insult everybody in it. Individually, personally, one by one, and (this was the thing he really decided to grit his teeth over) in alphabetical order. When people protested to him, as they sometimes had done, that the plan was not merely misguided but actually impossible because of the number of people being born and dying all the time, he would merely fix them with a steely look and say, "A man can dream can't he?"