Contact List View Search by Account Name

I have a customer who wants to be able to search the contact module in the list view by Account Name. 

I understand that they can use the filter to find what they need but I was wondering if this would work? I've tried it in a demo account but I think I'm missing something. 

Because Account Name is a relate field in the contact module its not full text searchable. 

Create a new field with a calculated value using this formula: related($accounts,"name")

Full text searchable

Reportable

Boost value above 1

Then I added this field to the list view and record view layouts. 

It's not working. Am I missing something?