Does this itinerary worth the 14 day pass?

Yes, you will save hundreds with the pass. (I estimate your travel expense without the JR Pass by ~700€) You might consider the 21 day pass by using google maps or HyperDia to get the prices for your first or last two days. In my opinion, Shinkansen are extremely pricey if you are using no JR pass.

Be careful not to use the Nozomi (express Shinkansen) between Osaka and Tokyo. Some of your routes won't be free with the pass as well, so you should either plan the routes beforehand or be prepared to pay an unknown sum when booking your seats upon arrival.

Thanks a lot! Only one more thing, which of the routes are not free with the JR Pass?

Parts of Osaka - Koyasan - Tokyo and Kyoto - Nara - Hiroshima are not operated by JR and will most likely not accept the JR Pass. I don't think they will cost much since the long distance routes are operated by JRs Shinkansen.

Maybe some employee will answer your question as well, since I'm a just tourist like you I won't guarantee that my statement above is completely accurate or complete. Either wait for a better answer or plan your trip using Google maps.

Have a nice trip!