No, being objective when it comes to history is not “doomed to fail”. Even the politicizers will get swallowed up by their own machinations.
I thoroughly expect within the next 20 years, that George Washington (the slave owner) will be struck from the history books, his picture taken off the dollar, and Washington DC renamed.
It is indeed doomed to fail.
I have been a student of history for 50 years. It is my daily reading. One can try to be objective, but we humans are too weak and ignorant to succeed. From experience, there is always a valid point of view from which one can criticize any work of history, on many grounds. Errors of commission are a risk, errors of bias, unacknowledged assumptions are a greater risk, but greater than any are errors of omission.
All histories are biased. The real question is whether they are useful, and for what.