I agree at the high level. STEM bringing general benefit and greater understanding of the world is the main reason. This is true whether or not humans or an AGI is driving the progress.

"It is not the destination, but the journey that matters"

For now, AI will be another tool in the toolbox of mathematicians. With humans driving the conversation to help understand the world better. If/when AGI is reached maybe we won’t be in the driver seat as much. I don’t think that matters. The goal of math is to achieve greater understanding of the world, regardless if humans are driving or if an AI is.

Why would my tax dollars go to fund someone's journey on what's essentially a hobby at this point?

Previous to you tax dollars and philanthropy have funded math in various forms and you reap the benefits.

You funded it before with your tax dollars, and it was already a hobby at this point. Mathematicians do what they do because it is fun. Well-paid-for fun, if they were able to get tenured.