It is much cheaper for a 23 yo to get their own insurance than to be added to the parent's one. Check the prices - you will be amazed.
Or you can stay away from being insured altogether.
for the price you have to pay you would be able to pay cash from your pocket whenever you needed it.
That is not necessarily true.
My last two employers charged one rate for employee + children. It didn't matter if you had one child or five children.
For example, say one has three children, a 17 yo, a 20 yo and a 22 yo. Obviously, that parent would have the 17 yo on their work sponsored insurance. If both the 20 and 22 yo are employed, with or without work sponsored insurance, it would still be cheaper to include them on the parents work sponsored insurance, since it costs the same regardless of the number of children. Were the 20 and 22 yo to seek other insurance, the net cost would be greater than adding them to the current family plan offered by the parents company.
I suspect that companies will soon change that policy of "employee + children" being the same cost regardless of the number of children.
BTW, the last two companies I've worked for is a 21 year time frame., so it's not a new thing.