CiviCRM and WordPress on different hosts?
There are multiple ways to do integration with CiviCRM.
CiviCRM and WordPress on the same server.
There are certainly benefits that come with hosting CiviCRM and WordPress together. Those benefits are a distinguishing feature compared to other CRMs that often lead folks to pick CiviCRM.  For instance, using Caldera Form-CiviCRM integration, or the CiviEvent widget.  Donation, membership and event signups automatically inherit your site's theme.  A shared login system.
CiviCRM and WordPress on different servers
Many folks choose to keep their website and CRM separate.  Sometimes the CRM contains data that necessitates higher security. Sometimes a parent organization offers CiviCRM to its branch offices, who wish to maintain their own website but use CiviCRM.
You can still do a good amount of integration.  There is Remoteform to do remote event/donation pages and email signups remotely (though not yet with 100% of features of a same-site page).  Contact Form 7 CiviCRM integration allows remote form submission.  I have a proposal in to synchronize events from CiviCRM to a remote (or local) WordPress site running Event Calendar Pro which I would release publicly if funded.  However, there's no denying these are more advanced configurations which are more difficult to set up.
The short answer
Ultimately CiviCRM requires a CMS, even as a &quot;shell&quot; to manage users.  If you're going to go with a host capable of running CiviCRM anyway, there's no reason not to switch your WordPress site to that same server and likely save a few bucks by canceling that hosting.