Reproduction is like a quest for immortality. We strive to "go on" somehow. If we all became immortal, there would not be any need to reproduce anymore. That takes care the "where to fit" issue :D
As of boredom, you are right. Life as we know it would lose its meaning. Perhaps it would gain a new one. Not reproducing would probably mean not evolving biologically, apart from artificial means. We would still have the same instincts that remain with us until now, no matter how many years would have passed. That could only change when we slowly turned into robots, replacing our brain neurons with artificial ones or uploading our conscience onto a computer. Would we still be considered immortal? Our human nature would have died.
There is no such thing as immortal :)