Yes, I access email, calendar and contact via browser only on all desktop computers I use. And on phones and tablets I use native Gmail and Calendar apps and have contacts synchronized everywhere.

I haven't used desktop client for private mail for years, and I don't see that changing, because of the privacy and security concerns. I'm willing to let NSA or some other faceless foreign entity snoop my email if that will prevent people around me that can get hold of my phone or computer from reading my mail.