Inventions could be publicly funded and then the findings be made available to everyone. We already pay for all the inventions we use indirectly so why not just fund them to begin with and actually have access to this information.

That's what academia is for. Perhaps we should ensure that academic research that is publicly funded doesn't end up with IP restrictions placed on it, and also expand the range of research academia engages in, to include more applied-research stuff and rediscovering/popularizing existing know-how that often is not publicly documented and might not even exist other than in tacit form. (This expanded scope for research would also help reduce waste due to academics overcrowding into a few über-popular fields of research, and largely duplicating efforts while trying to "scoop" one another.)

Of course, tacit know-how and first-to-market advantages will always exist to some extent. So, in a sense, we can't fully get rid of "IP"-like dynamics. But we can, and should, mitigate them.

And where are these unlimited funds you speak of? I have a few crazy ideas of my own, that I'm willing to pursue on someone else's dime.

We have the ability to automate almost everything needed for life. It seems realistic that you could spend all your time working on crazy ideas and cost no one a minute of their time.