Fatal error: Uncaught exception 'mysqli_sql_exception' with message 'No index used in query/prepared statement'

The fatal error is not in MySQL; the missing index notification is a relatively low-severity warning.

The fatal error is in your PHP code, because of the following three conditions:

• mysqli reports a lot of warnings, even for relatively harmless conditions.
• You're throwing mysqli_sql_exception for all errors and warnings due to your mysqli_report(MYSQLI_REPORT_ALL); line.
• Your PHP code is not catching that exception (i.e. it's not in a try{} block with an appropriate catch(){} block), and uncaught exceptions are fatal.

You can't do much about the first one, as mentioned in the other answer. So, you can fix it either by changing your mysqli_report(...) setting to MYSQLI_REPORT_STRICT or MYSQLI_REPORT_OFF, or indeed anything other than MYSQLI_REPORT_ALL.

(edit: w3d's comment below gives a good explanation why, and suggests you could use mysqli_report(MYSQLI_REPORT_ERROR | MYSQLI_REPORT_STRICT) as a good alternative)

For best practices, and in combination with this, you should fix it properly by using try{} and catch(){} appropriately within your code.

mysqli_report(MYSQLI_REPORT_ALL ^ MYSQLI_REPORT_INDEX);

Turns off "Report if no index or bad index was used in a query" yet keeps other reporting on.

Take a look at this bug-report : #35450 mysqli extension reports too many warnings

Quoting a few sentences of a note :

Mysqli extension throws too many warnings.
For example, "SELECT * FROM table" results in a warning: "Warning: mysqli::query(): No index used in query/prepared statement SELECT * FROM table ..."

And, quoting another note, which seems interesting :

Use mysqli_report() to disable that.