The main reason I avoid tables is because of my previous experience. Tables, and especially nested tables that wrap the entire site, would be noticeably slower when changing styles dynamically. For example, changing the positioning of an element on hover when the element is deeply nested in divs. The second I removed the tables, this was calculated much faster. This was about five years ago so I have no idea if this performance concern exists any more.

Separation of concerns is a design choice. I'm not sure what context you meant, but if you find that it's overkill, you can make that design choice that it's unnecessary. In general, I find separating these concerns leads to cleaner and more understandable code, but I can certainly imagine situations where your argument can be made, especially on sites that are simpler.

Some people do believe quite a bit in purity and believe the markup should just describe the data. I agree that it's nice but doesn't always work out in practice. This can get taken too far. For example, I've seen complex workarounds for centering vertical alignment when they could have just thrown a table, but they wouldn't do it because a table is for tabular data. In this case, I felt that the table would have been easier to read and understand. Again, this is my preference and others may disagree.

TL;DR; - It depends. And performance issues back in the day.