This is a good point. But of course the online (web) version won't have the features or easy accessibility as the App. What would concern me most is privacy, control, and storage space where your data is stored in their cloud vs. on your own device. But for sure the online version is a viable free option for many.
I personally to be honest do not wonder about storage. Microsoft storage (OneDrive) is secured. Otherwise most companies and corporations would not use it. Any big enough corporation conducts their own security audit for every tool they use. I know that my company does it (granted we are also into IT). If we had concerns with OneDrive and we would not use it for our business.
What people should know about though is that the online versions of the apps do not offer all functionality. Some options that we are used to in the desktop version are missing from the online version. So