I just ran your setup in LTspice with the similar 2N2222 and I see 400mA into the base - already huge. Thermal runaway will make this much larger in real life. I think you have something set up wrong.
As for your recent question, yes, it can switch on just fine, because the base-emitter voltage (or current, depending on the model) determines the collector current. VBE is not exactly 0.65V, it varies with applied current. The more current you apply through the limiting resistor, the higher the voltage goes, and the more current the transistor will allow to pass into the collector.
Just like a diode, there is no fixed voltage drop, voltage varies with current. (Or current varies with voltage.) But if you plot a graph of current vs. voltage, there is a sharp corner around that 0.65V, and the current drawn shoots up fast. You could in theory apply the proper voltage directly to the base without a resistor, but it would be something in the 0.65-0.9V range. (With a 2N2222, LTspice gives me a range of roughly just about 0mA to 300mA for that voltage range.) In real life you need the resistor to protect against variation in this I/V curve (it varies from transistor to transistor, but also varies significantly with temperature), and it also helps you hit that tiny voltage more accurately.
Try it in LTspice. Apply a voltage {VB} directly to the base (include the curly braces), then add a directive (Edit -> SPICE directive) ".step param VB 0.65 0.9 0.05" (make sure to include the dot at the beginning, do not include quotes), and run an operating point analysis. Check the collector current. Try the same thing with a steady voltage, but add a varying resistor (you can vary resistance the same way as voltage - .step param PARAM_NAME LOW HIGH STEP_AMOUNT")