Is it really necessary?
Depends. See:
I'm being told by some staffing companies that I need a 1 million dollar business insurance to
work with some of the companies around my area.
What is your question. Want to do business with them - get insurance. Otherwise - don't do business with those companies.
Plus, what the heck do you complain about?
Ocne upon a time I needed a business insurance for a project - I think around 3 million USD or so. Was about 20 USD per month. Not even showing up on the cost side after rounding.
If so how do most tech start ups deal with this?
They do not because they don't do work for hire. Most tech startups are not selling their services but try to develop a product. You are not a startup. You are a web developer that tries to build an agency - something most people would not consider a startup by any means.
Most of the time I just get a contract that does not get me any liability. But then, I am not a web developer - in my area of expertise, getting someone is the problem. As web developer, getting customers is likely the problem.