Companies should trust the people applying based on their resume and ability to talk about what they have done in the past or how they would approach real world problems (organizational, interpersonal, technical). Maybe have them write some small bit of real world code using libraries and frameworks they are familiar with, while they are alone without anyone watching [key|pen]strokes.
Maybe I'm lucky but after 20 years in the industry shipping products to consumers I've never ran into a Software Developer or "Engineer" in the real world that couldn't get things done in a normal working environment in private industry (now in government, don't get me started). Some are slower, some are faster, some can handle bigger problems, but I have no idea how to reliably filter for that in an interview having tried many things.
The "OMG this senior person can't write FizzBuzz on a whiteboard or while videoconferencing and knowing someone is watching your every keystroke so they must be a horrible programmer" approach is just wrong.
I've only ever failed interviews where I had to solve problems or write code with someone watching (virtually or in person). Let me be alone and give me a product to build, though, and it'll get done. Customers will love it and it will be great. See: resume and products in the wild. The Math-oriented abstract tech interview is missing out on all the practitioners that care about the product and can build reliable maintainable systems in a team environment.
These days I'm primarily management, though, so I get to set the hiring guidelines. Yay!