Need based funding vs Valuation based funding

I have come across several situations wherein the VC invests based on funds needed to get certain things done in a startup.This seems ok, but most will want nothing less than 20% of the company.

Let me give an example. Say you are trying to raise 5million. As per the VCs assessment you can cut it down to 1 million if you just invest in the most important things for now. Assume the suggestion makes business sense and you are ok with it.

Now you would expect that the VC takes only one fifth of his original share since his investment is one fifth.But no, the VC wants the same or only slightly less piece of the company.

What surprises me is that nobody raises this question -

As a founder, I am parting with x% of equity, the amount raised for the same should only be a function of valuation of the company and not what I need. You may choose to invest a lower amount based on your assessment but the share would be proportionate to the investment.

Note: This is in context of the Indian Startup eco system. The observations are from information available in the public domain such as blogs and videos covering startup events, pitches etc. The focus is on startups in their early stages.

There are a lot of steps in the valuation dance, but in the end, it all boils down to "I'm willing to give you $X in exchange for Y% of your company."

If the VC originally agreed to give you 5 million, but now only wants to give you one, it seems that you should only give him 1/5th of what he would have originally gotten and it certainly seems shady that he's not willing to take a cut in his percentage. But, he can always walk away if he doesn't like the deal.

You do need to be careful, though; here's what I see: You've given up on a significant chunk of your flexibility because you've agreed to do what the VC wanted, and you're only getting 1/5th of the investment you would have originally gotten. How much more is the VC going to try to tell you what to do? When you need the second million, what strings will be applied?