That is baseless bullshit. I have been using the same 10mL 40mg/ml vial for over a year and there is no "contamination". If you're drawing with a huge needle (think 18G), then u can core the vial, but I draw with a 30G needle and there is essentially zero risk of that. All you need to look out for is if the solution turns cloudy, which indicates that the oil (castor, cottonseed, sesame, or sunflower oil, usually) is breaking down, and the estradiol is precipitating out of solution. Unless you get a really bad/old vial, or you leave it somewhere that it isn't protected from UV, or that isn't properly temperature controlled (estradiol precipitates out of solution at cold temperatures), that won't happen during the time you have the vial. Shelf life is 3-5 years for well formulated estradiol.
The reality of the situation is that insurance and pharmacies only operate on a monthly basis, so they dispense you a new one each month. It's laziness and wastefulness.