Sounds good to me too since I copy paste from there time to time and also an unclosed connection doesn't seem to trigger a ResourceWarning it seems. I have pushed a commit to the same PR. I have changed it manually for all the include files. I have ran the files after the PR with the below and I couldn't see any breakages. Let me know if I have missed anything in the include files. I guess there are some more examples in sqlite3.rst but I don't know if it needs to be added on all snippets since they are more focused on the particular function unlike the files in the include folder that has full programs.

Verified with : 

$ ls -1 Doc/includes/sqlite3/*py > sample.txt
$ cat sample.txt | xargs -n 1 ./python.exe

Thanks