How should you respond to job recruiters who outright approach you asking for your last drawn salary? Why would they do that?

This is called "qualifying". Why? Because:

• if your salary falls below the range of salaries that they recruit for, you're not eligible

• if you salary falls above the range of salaries that they recruit for, you're not eligible

• if your expected is above a certain % from your salary, you're not eligible

• if your salary is already close to their budget, you're not eligible

and a myriad of reasons on their end.

At the same time, you also have multiple factors to consider on your end, with salary being a very important one and usually a dealbreaker in some situations.

I prefer this instead to be honest, so that we don't waste each other's time. However, I would be upfront about it only if the recruiter sends a JD beforehand and there is already a 65-80% match for the requirements/skillset. You can tell when someone is just mass-sending.

This is a no win situation. You don't have to give your last drawn salary if you don't want to but similarly, the company doesn't have to interview you either of you don't.

It's really up to you how you respond. For me, I just round my salary up and let them know what I would expect moving forward(usually 10-30%)
I tell them my salary because I believe that I am good enough to warrant that 10-30% increase with my CV, current experience and any relavant courses/certifications.

If they reject me only based on the asking salary, then I probably wouldn't like the company culture so it's not a big loss for me.

On a side note, while I do understand your frustration with the recruiters, I do feel it is not entirely their fault as some company's won't even look at their candidates if they don't have that info. Of course if they are rude or confrontational when you choose not to reply is a different story but with the current work culture of sg, I don't think you can avoid giving your salary without limiting your options.