Are they the two main reasons why I never got a good steak crust?

Neither of those sounds like a big problem.

You say that you get your pan "really hot". It's nice to use an infrared thermometer to check how hot, but at the very least, you should check for the Leidenfrost effect: if you put a drop of water on the pan, it should skitter around without visibly boiling, and take several seconds to actually evaporate. That means your pan is at ~200 Celsius or higher.

The problem is, the moment you put your steak on the pan, that temperature drops precipitously, because the water in the steak will be boiling away. If your burner can't put out enough power, you won't be able to get a good crust no matter what the initial temperature is. If your burner puts out almost enough power, then using a cast iron pan can help because it has a high thermal mass to transfer to the steak, but even there you're limited. Always use the largest burner you have available, even if it's bigger than your pan.

Not letting the steak come up to room temperature is not a problem. Actually, it helps to have it just out of the refrigerator, because the surface of the steak can spend more time hot (and crusting up) before the center overcooks.

Only using a small amount of oil is probably not a problem. If you're using a non-stick pan, using more oil can help you get a more consistent crust rather than only parts of the steak crusting up. But the oil by itself won't make the difference between brown and grey.

Finally, if your primary concern is the crust, make sure you only flip the steak once. Flipping it multiple times helps you get more even cooking, but what you're looking for here is really uneven cooking. The first little while after you flip the steak, the bottom surface needs to come up to Maillard browning temperatures. The more you flip the steak, the more of the cooking time is wasted in that "getting ready to brown" stage.