It depends on where you are in terms of the compensation spectrum. It can definitely lead to bias if your current salary is not on the higher side.
For too long, I have played this back and forth game of revealing salary and asking them for budget and frankly, it’s too tiring in Indian recruitment circles.
So, I have started just being honest from the beginning about my current pay & expectation and have seen recruiters be transparent about their budgets too.
Eventually if a company has to lowball they anyway would, but I am glad that I don’t have to exercise so much cognitive effort playing this game of riddles