so under the assumption that HT and TH have equal probability that method seems good for eliminating bias but there is that assumption.
That's not an assumption - it's pure math.
Let's say your coin is biased to 60% heads, 40% tails. The probability of HT is 0.6*0.4 = 0.24. The probability of TH is 0.4*0.6 = 0.24. The probability is identical. This is the whole premise behind von Neumann's algorithm - you
know HT and TH are equally probable without the need to perform any statistical testing of your coin.