Just to be clear - the things you actually care about expressing in a program don't require Turing completeness about 99.99999% of the time. The main exceptions are things like unbounded searches where the code will only terminate if it finds a solution to something, and there's no a priori size bound on the solution space.

We use Turing complete languages as a compromise. Proving your algorithm terminates to the satisfaction of a proof checker is often more work than it's worth. We've decided allowing bugs that a termination checker would prevent is less work to deal with than satisfying a termination checker. But for my daily work, Turing completeness is a practical compromise, not a necessity for expressing the algorithms I need to.