IME you could have gotten the higher number if you'd avoided saying it.
Because you surrendered a number almost immediately, they have decided that you're inexperienced and so deserve less money.
I think a better strategy is to not answer: "OK, I think it's fine if you don't want to talk about salary right now. I'm sure you pay competitively. Let's focus on whether I'm a good fit with the team first."
After the engineering team has told the recruiter that they want to move forward with hiring you, you have more leverage to negotiate.
If you're finding that your opening bid is always rejected, it's probably because you don't know what's a good number to name. (Lots of people sneer at this but I don't think this is some failing on your part--companies pay tons of money for this kind of salary data which is how they know it.) In this case, you should just do anything you can to avoid naming a number first.
Sorry, I guess my brief summary wasn't clear, I basically do what you say and avoid the discussion as long as possible. You are 100% correct you are in a much better position when the technical folks want you vs some random recruiter.
Because you surrendered a number almost immediately, they have decided that you're inexperienced and so deserve less money.
I think a better strategy is to not answer: "OK, I think it's fine if you don't want to talk about salary right now. I'm sure you pay competitively. Let's focus on whether I'm a good fit with the team first."
After the engineering team has told the recruiter that they want to move forward with hiring you, you have more leverage to negotiate.
If you're finding that your opening bid is always rejected, it's probably because you don't know what's a good number to name. (Lots of people sneer at this but I don't think this is some failing on your part--companies pay tons of money for this kind of salary data which is how they know it.) In this case, you should just do anything you can to avoid naming a number first.