Titanium got replaced by carbon, because carbon is
- cheaper (compared to titanium, which was hugely expensive)
- lighter
- stiffer
- better ride quality

...all together (with a well designed carbon bike).

The only holdout was concerns over longevity, which despite the fear mongering doesn't seem to have played out - after a decade or two, well made carbon frames haven't seem to be an less durable than their previous non-carbon counterparts. Frankly, the topic of carbon durability has been discussed 3 times this week, so I have no intention on posting about it a 4th time. Someone always has an anecdotal story about some carbon component breaking, someone comes back with an ancedotal story about a steel/aluminum component doing the same thing. There's always some sort of fearmongering about how the frame won't last more than 5 years, but frankly last year I was searching on the topic and found a thread on bikeforums saying the same thing - except about steel vs aluminum. A bunch of people arguing your aluminum frame is never going to last more than 5 years, it's going to fail suddenly and catastrophically, etc etc etc. Nowadays aluminum is supposedly long lasting, but carbon won't last...you get the idea. If another material comes out in 20 years, then carbon will be durable but that new material won't last.