In my personal digital life I have successfully removed the need for native apps that handle my email, contacts, calendars, notes, to-do’s, etc etc and instead relied purely on the browser to handle the task.
I extended this accomplishment to my professional digital life and all was working well at first, but it soon became clear that handling 400+ emails and many calendar invites on a daily basis via a browser is rather cumbersome. Therefore I have reverted back to native applications just for handling my emails and calendars. Everything else I do is still in the browser and thus far have had no issues with it.
All my work stuff is done on the Mac, so I am utilizing the standard Mail.app and iCal applications. Will keep an eye out for anything more superior, but these seem to do the job very well.