BMX bikes have really long crank arms. They are intended to be ridden while standing, jumping, doing tricks, etc...Using the seat for sitting will put the kids knees in their chest while riding. Hugely inconvenient & impractical.
A kids bike should be able to be pedaled around the cul-de-sac.
Check your local Craigs-marketplace-offer site. Kids bikes are a dime a dozen. Jett makes some pretty decent aluminum lightweights. A Trek Precaliber might be a bit cheaper. Specialized HotRock will do the job too. I think Giant does the ATX.
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I shouldn't have to "make myself more visible;" Drivers should just stop running people over.
Car dependency is a tax.