Here are my steps to reproduce using ProcessWire 2.6.1. Will you please give it a try?
1. From menu, click Setup -> Templates -> Add New.
2. Input template name, e.g. "justonepage".
3. Click Add Templates.
4. From menu, click Pages.
5. Click New next to Home page.
6. Input title, e.g. "Page Uses My Single Page Template".
7. Choose template from step 2.
8. Click Save.
9. From menu, click Setup -> Templates -> (name of template from step 2).
10. Click Family.
11. Select "No" for "Can this template be used for new pages?".
12. Click Save.
13. From menu, click Pages.
14. Click New next to Home page.
15. Input a title, e.g. "Some other page".
16. Click Save.
17. Click Settings.
18. Click the Template dropdown.
The template created in step 3 is present in the droplist.
Thanks!