Hosted email often comes as part of another service, such as web hosting or Infrastructure-as-a-Service (IaaS). Since that means there will be many extras available with these services, it's inescapable that you'll be paying for those extras in some way. Purchasing them usually means a slight uptick in that per-user price. Many businesses find that, once they're done selecting all of their needed "optional extras," their end price can often reach as high as $10 or more per user. This can start to add up for larger teams. It's somewhat like buying cable service: sometimes you need to pay for the channels you don't want to get the couple of channels that you need. There is also the old adage that "you get what you pay for" when it comes to quality. This is almost always true when considering an email host.
That's a big difference, with "inbox zero" requiring an email client with great archiving that works over multiple device types. Meanwhile, at the other end of the spectrum, the personal information managers need something more like Microsoft Outlook, with excellent search capabilities as well as a good storage contract on the hosting side because these types of inboxes are often tens of gigabytes (GB) per user.
One of the most important compatibility factors to consider with email is the mobility question. How often do your employees need to access email via mobile devices? That's an important issue because most email hosting providers deliver some kind of web client usable as a default inbox. Almost all of these can be accessed via a mobile device, so if your employees don't need to access their emails on the road that much, then such mediocre clients are probably fine.