I thought about float valves but it seems unnecessarily complicated to build. I'm trying to use the stuff I already have. I did find some 33cent felt today to use for the wicks.
If you want to go without any valves, you have to wick the nutrient directly from the reservoir. This works, of course, but it is limiting compared to getting the nutrient from a central tank. You cannot wick over arbitrary distances.
I think you should take a look at Hoocho's channel on YouTube. He shows how to make some superb wick systems for almost no money.
These float valves I'm talking about cost less than $5 on Amazon, it's really not an addition that should push the project over budget...
You can make something like Hoocho's setup with a couple of PVC pipes, said $5 float valves, a few net cups and some basic tools. But then you'll already end up with a system that can easily host several plants and will be extremely flexible.
I think the design of an AutoPot or Hoocho-setup is already about as simple as it gets, while still giving you a very high performing, fully-automatic solution. If you want to make it even simpler, e.g. by leaving out valves completely, you will end up with manual work and/or an unreliable system.
Also I think you should be willing to spend maybe $60 on your irrigation system, it will pay itself off immediately anyway, and you will be surprised how much hassle it will spare you. Plants will be healthier, too, because there is no room for watering mistakes.