Your description sounds like this should only be a problem for families with serious medical issues, which would be the minority. I do have a kid. If your kid is relatively healthy then pediatricians are basically replaceable widgets. If it's important to you, just pay the cash rate for your favorite pediatrician during that 3 month period. If you're really hung up on it, you can just choose the COBRA option and keep your old insurance during your trial period. It's very expensive, but again, you just calculate that into your contracting rate.
>And keep in mind it's definitely a seller's market if you're a good dev. It's incredibly unlikely that the 3-month contract is the only offer on the table. So all things being equal, who would take it?
I don't feel any additional security whatsoever being a least tenured employee vs contractor. Maybe there's some statistical benefit, but it seems pretty small. So for me, it's practically zero cost to do the contract-to-hire thing. Any financial costs are just built into my rate. I'd rather spend my hiring currency on other stuff like working remote full time and extra vacation days.
It probably makes a difference that I spent a big chunk of my career as a self employed consultant. I do remember feeling some anxiety when I first transitioned from a regular employee to consulting. But I quickly learned my anxiety was unfounded.