Letting the List view search bar find tasks by task name, task description, and Custom Fields is a great idea and super practical.
It would be even better if the "Relationships" Custom Field were included in that search too.
I used to use a "Dropdown" Custom Field to indicate the company of the task (each option was a company). But since there are so many companies, when the new "Relationships" Custom Field came out I replaced the Dropdown. Now I have a list dedicated to companies, and I use the "Relationships" field to link each task to its company in that list.
Unfortunately, I'm thinking about switching back to the "Dropdown" Custom Field, because I found out you can't use the search bar to search tasks by the "Relationships" field, and I always use the search bar to find tasks with the same company.