I'll warn you that insurance companies often try not to cover a loss or all of it. They often try to cheat their customers. So, having insurance isnt equal to a structure that makes you personally immune to liability because what the insurance company will do is unknown.
And I'll warn you a limited liability entity doesn't necessarily protect your personal assets either.
Undercapitalization is a big one that people don't often realize - going without insurance an not enough funds to cover a claim will usually pierce the veil.
Same goes with little things that typically don't matter to the owner of a one person company, like failing to keep board/member annual meeting minutes and sending them to the state body that requires them, and the biggest one for most small businesses - commingling funds and "alter ego" doctrine - the company is not you, the company's money is not yours.
There are a lot of ways that limited liabilities vanish - especially for smaller businesses like OP is describing.
