I think you are wrong. Yes, better understanding of hardware implementation (cache sizes and latency, branch prediction and pipelines, specialized instructions) is important. But also in real life those asymptotic complexities will often have similar c and N_0, or your input will be bigger than N_0, so O(n) vs O(n^2) will still matter. Basic analysis of algorithms makes your life easier because, in this simplified model, you can get a rough estimate of time/space requirements. Of course, if you have competing implementations, you will benchmark them (which is not straightforward to do properly).

By the way, usually we use "complexity theory" for a part of theoretical computer science (math) concerned with proving lower bounds (like the most famous P vs. NP). What is required for basic analysis of algorithms (without any fancy methods) is not very hard. Yes, you can search the web like we all do, but first you need to know what are you searching for. Also, we reuse algorithms/data structures but not only in the final product but also in our own new algorightms so you cannot search it.

Regarding interviews, I think the main problem is that many companies and interviewers try to blindly copy the questions (cargo cult) without understanding the point of such interviews. The point IMO is that you evaluate analytic skills of a candidate. Correct/incorrect answer is not everything. You could do the same with math, science problems but algorithms/data structures are closer to programming. Anyway, I feel this is becoming a controversial topic.