What are some major examples of successful derandomization or at least progress in showing concrete evidence towards $P=BPP$ goal (not the hardness randomness connection)?
The only example that comes to my mind is AKS deterministic polynomial time primality testing (even for this there was a methodology assuming GRH). So what specific evidence through example do we have for derandomization (again not the hardness or oracle connection)?
Please keep examples to only where time complexity improvement was shown from randomized poly to deterministic poly or something that is very close for specific problems.
Following is more of a comment and I do not know much it will help this query.
Chazelle has a very intriguing statement in http://www.cs.princeton.edu/~chazelle/linernotes.html under 'The Discrepancy Method: Randomness and Complexity (Cambridge University Press, 2000)'.
'It's been an endless source of fascination for me that a deeper understanding of deterministic computation should require the mastery of randomization. I wrote this book to illustrate this powerful connection. From minimum spanning trees to linear programming to Delaunay triangulations, the most efficient algorithms are often derandomizations of probabilistic solutions. The discrepancy method puts the spotlight on one of the most fruitful questions in all of computer science: if you think you need random bits, please tell us why?'