Re: flat tires. Some tires are made to be resistant to punctures. I've used Continental Gatorskins and have been very happy with them.
When I first got a road bike, after riding a mountain bike on both dirt and pavement, I felt very unstable. It took a few rides to get used to the thinner tires and different geometry. I suspect most people need to adjust to the different feel when they first get a road bike.
As for carbon frames, yes, sometimes they do crack, but that would happen because of a crash or some other impact on the frame. You can examine your frame and forks before every ride to make sure there are no abnormalities. I personally look the frame over whenever I clean the bike or clean and lube the chain.
- Gray 2010 carbon WSD road bike, Rivet Independence saddle
- Red hardtail 26" aluminum mountain bike, Bontrager Evoke WSD saddle
- Royal blue 2018 aluminum gravel bike, Rivet Pearl saddle
Gone but not forgotten:
- Silver 2003 aluminum road bike
- Two awesome worn out Juliana saddles