R Avraham Yosef (the son of R Ovadia Yosef) recently said on his weekly radio program that, in his synagogue, he always call up 10 people on Shabbat to ensure that at least seven of them are Shabbat-observant.
I had never seen or heard this before. I know there are opinions (e.g., here) that one should not offer an alyah to a non-observant person. But in synagogues I went to, even when calling non-observant people (e.g., the family of a bar mitsva boy), they always stop at seven.
What is the Halachic basis for the idea that a synagogue needs to ensure it has seven Shabbat observers getting called up? Is this more common amongst Sefaradim? Have others seen this?