The company that hired me as an independent contractor didn't get paid. Should I expect payment?

I'm an independant contractor, but the company I did work through was not paid by the client despite me performing and completing all necessary tasks to a high degree.

Should I still expect to get paid by the company? After all, I was to be paid by the company and not the client directly, so what the client does is irrelevant to my contract as independant contractor. Is that the correct way to view this situation?

You have exactly the right perspective on this situation. I trust that you have a written contract that defines what and when you are paid. (For example, $30 per hour payable weekly.)

Some contracts pay at the end of a project; but if I were you, I would require more frequent payment.

Regardless, if you provided the services that the contract specified you would and/or that you were directed to provide, you are owed the amount agreed upon. It is immaterial whether the company through which you worked was paid or not.