Actually, most app sandboxes have to request network access as a permission. Unfortunately most mobile OSes don't let you deny it at present. However, you have a lot of options for using network devices or inspection software to intervene and block requests on local machines. Meanwhile, once data is on a remote server, you have no control of it.

Furthermore, native apps can be retained and often installed after they're no longer supported by their developer. Web apps vanish into the night, and leave you with nothing.