As a senior programmer, I couldn't agree more with almost everything you said. I lead projects and solve problems for both product and code on a daily basis, amongst dozens of other random tasks. Almost never do I encounter brain teaser trick questions on how to find the middle value of a linked list, and if I do encounter such a weird situation, I very efficiently google for an answer. There is no way (or need) to keep all these 'solutions' in your brain throughout your career. Sure, give me a month or two to practice leet code problems and I too will pass your test, but I'm an adult with kids, I don't have time to waste studying for things I will never use just to pass a meaningless exam.

I think even better than a code review is a long conversation about code/programming in general. Discuss code best practices. Discuss job tasks handled in previous jobs. Ask how to decide which technology to use on a new task. Ask about implementing a 'language' they have never never used before. Ask about tooling and when to pay for something vs when to build something in-house. Etc...

Through a conversation you will learn so much more than you would in any kind of 'test' environment. You will learn their knowledge base and skillsets, their enthusiasm for the job, and probably most importantly, how you will be able to communicate with this person in the job.

If any code is required - a very small take home project with a week or two deadline would be preferred. Then you can see how they code and architect something from scratch. Even if they have to google to find out 'how to do it' - so what - if they do that on the job, they meet the deadlines, and you like the result, congratulations!