Was this a glass test tube? I understand why glass is probably the best material for the inner lining of containers that hold biological material, but I'm surprised that there aren't better solutions for hazardous material (e.g. an unbreakable, transparent polymer outer coating).
Or a double wall - one glass one polymer
There is regular soda-lime glass and there is borosilicate glass.
I believe the biggest reason to use glass is that it doesn't react with much stuff, but I've yet to see an explanation for why your idea wouldn't work. I imagine there could be problems with autoclaves (i.e. degradation of the polymer) and fear of chemical leaching.