I know very few people, even in IT, who have full-featured back-ups of their home systems. Even fewer have easy, convenient remote access to their data.
Using online apps with online data services give you both of these things 99% of the time. They are a better option (assuming they have the features you need) than running things locally for the vast majority of people. Yes SaaS/cloud services might screw up, but the chances of them doing so are far lower than the chances of YOU screwing up.
You are basing your decision based on anecdotes, not on statistics or evidence. Gmail's backup system is better than yours. Their remote access is better than yours. Use the brain your ancestors evolved for you. It can reason based on probabilities rather than bullshit if you let it.