The answer is because of how much (or little) background is needed to understand each concept.
For example people don't develop intuition into what an exponential with a complex power should be until after have been introduced to it through power series. But understanding why those power series mean what they mean requires understanding the power series for e^x. Which means that they need to already understand e. Therefore you need to introduce e before you introduce exponentials with complex powers - you can't do it the other way.
That said, you will occasionally encounter mathematicians who advocate for teaching about e by first demonstrating that 1/x has an integral, calling its integral ln(x), then demonstrating that the inverse function to ln(x) is an exponential function and calling it e^x. The argument for this order of presentation is that we can present every step of this with mathematical rigor. The argument against this order of presentation is that students find it very confusing. And very few students will ever notice the logical gaps in the usual presentation.
For example people don't develop intuition into what an exponential with a complex power should be until after have been introduced to it through power series. But understanding why those power series mean what they mean requires understanding the power series for e^x. Which means that they need to already understand e. Therefore you need to introduce e before you introduce exponentials with complex powers - you can't do it the other way.
That said, you will occasionally encounter mathematicians who advocate for teaching about e by first demonstrating that 1/x has an integral, calling its integral ln(x), then demonstrating that the inverse function to ln(x) is an exponential function and calling it e^x. The argument for this order of presentation is that we can present every step of this with mathematical rigor. The argument against this order of presentation is that students find it very confusing. And very few students will ever notice the logical gaps in the usual presentation.