I mean the padauk stuff is not really a very beginner friendly environment, and it's not as cheap to get going once you consider the accessories needed. just buying and re-using an arduino or a knockoff for a couple dollars would probably be better if you wanted to make the case that a microcontroller is a better place to start.
1. For jellybean ICs "less than [US]$1" understates the case by about an order of magnitude; it's less than [US]$⅒.
2. Other ICs mentioned like the CD4017 have ceased to be jellybean parts and have become esoteric specialty parts, but they're still less than US$1, if you can find them.
3. The reason for this is that, as microcontrollers have gotten cheaper and more capable, the range of circuits for which they are a good fit has grown enormously, and in particular covers just about every circuit where you'd use a CD4017. And once you have a microcontroller in your circuit you probably don't need a 4017 or a 555 because you can usually replace them with 1–5 lines of code.
4. Probing line power with a questionable-quality multimeter really is dangerous.
Does that clarify?
I agree that Arduino is a much more beginner-friendly environment, even more so than quasi-analog DIPs in a breadboard, and also that the programmer hardware for the Padauk μCs is a significant obstacle.
The biggest reason I wouldn't use Padauk microcontrollers is that they're not available in north american distribution.
I personally really don't get the 555 timer love - almost anything people would do with one for a small design with no firmware, I would use an lm339 type quad comparator. They are great for detecting the presence/absence of pulses though.