There is simply no way for me to be involved in all the politics I would have to be involved in if we had direct democracy due to the circumstances of, well, living. I have neither the time, nor the resources, nor the literal energy to be completely politically engaged in all the decisions that are going to affect me, personally (again, if we had direct democracy).

I imagine I'm not alone in this (which is probably why we have indirect democracy in the first place). At the end of the road, direct democracy is knee-jerk democracy -- without having the time to contemplate on what you're voting for (which you invariably will not have due to the sheer amount of decisions to be taken all the time), the only option is to vote simply based on a gut feeling for the vast majority of the time.

Is that really a solid way to build a democratic system? I doubt it.

As an aside, calling an indirect democracy "undemocratic" is unnecessarily binary. Sure, direct democracy is more democratic than indirect democracy (however uselessly so), but indirect democracy is more democratic than, say, an absolute monarchy. That's just to say there's gradations. I wouldn't call a system that allows for citizens to steer the political agenda "inherently undemocratic".

Finally, though, I'd point out that your depiction of indirect democracy is very cynical. I'd invite you to come up with a few positives of indirect democracy; I think you'll find it's not so bad.