Which leads us to the "why" of it. Which is you wanted to monetize the site (if only to cover its costs.) Since advertising seems to be the business model of the internet that's your first port of call.
But here's a site that performs a task. Quite who uses this site is unclear. Sure lots of people might use it (for some definition of lots) but the site doesn't really give signals to adsense.
Conversely Adsense sells ads based on "targeted users". Which means your original site is pretty useless to Adsense.
Ok,I'm simplifying here, but what ads do you think -should- be shown to your visitors? Ads derived from their browsing history of sites that do intuit user context?
Are users browsing an arbitrary rubbish website more or less likely to be distracted by some special offer? Are people visiting your site to do some very specific task, presumably for a concrete reason, more or less likely to be distracted by an ad?
The problem isn't Google. The problem is that our ability to monetize the web starts and ends with adverts. Which means that sites that "do stuff" are a bad match, and therefore lack funding.
To be honest, I don't have a cunning plan of alternate funding. Probably the only other viable one is "take some of your day-job money and effectively sponsor the site yourself." Which of course is the model you -were- on that you wanted to leave.