Cheap Active/Passive Full-Range Speaker

I am looking for a cheap simple system for the kids to play around with.

A quick search gives party speaker systems at different prices but you have systems as The box PA 15 DSP as well. A Bluetooth speaker is easy to use but membrane area adds some significant punch in the sound.

Are there better alternatives than the PA system above in that price range?

I think a diy project will be more expensive even if the sound could be better with proper designed speaker cabinets. Only the speaker element will most probably be more expensive than these cheap active systems.
 
Depends on your salvaging abilities. Back when I was a kid I was plenty satisfied with a BTL chip amp salvaged from a car radio, a couple extras transistors from the junk box for gain, an 8 inch “ceiling speaker” and a 12 volt gel cell. In a wooden case. The most expensive thing was buying the mic. Not much more power than a Bluetooth speaker, but when you use even a 90 dB/W speaker (ie, BOFU clone) it will blow away a cute little 4” 82dB/W driver. Plenty loud enough to annoy the neighbors.

If you wanted to duplicate a $200 Behringer powered speaker using all new parts it would cost $800. And be overkill, and likely be killed before it was over. Not a good investment.