Sure, it's possible. But having met a few founders, their lifestyle from taking VC money seems far preferable to the bootstrap approach. It's true that you have to grow, but if you have growth, then nothing else matters. And if you don't, then you're one of the most employable people in the entire world.
A shocking number of people, somehow, end up in insane amounts of debt by trying to start their own companies. And you're sort of forced to. An example: one of our family members had a lucrative pole barn business. (Apparently in the midwest, lots of people wanted pole barns built, or something.) But in order to pay his employees to go construct the pole barns, he needed loans, leveraged against the future income from the construction project.
Then 2008 hit. Poof! Contracts all went poof. And he was left holding the bag.
So, if you need employees, and you're bootstrapped, how exactly are you going to pay an engineer roughly $130k per year? (Remember, the fully-loaded cost of an employee is much higher than their salary.) Loans must be so quite tempting.
And sure, LLCs are designed to mitigate personal risk. But that implies you can find someone willing to risk loaning to you.
I'm not saying that VC is great, just that it fills a need.