Are you a member of the wrong club? Not necessarly. May be that you can substiture another extension that does display k2 for the one that doesnt.
does it make sence to use mixed content? quoted from Jen4web " it depends"
Many people do that, use articles for what they are best for, and k2 items for what they are best for.
If your K2 ready template has a built in category, item, and user k2 override built into it and styled to match the site i would say its k2 ready and much of the work to customize has been done for you
If you have specific questions about a specific extension please ask, and remember all the above is IMHO