Computational power if..

I've just recently started to really grasp and understand the implications blockchain, when it comes to putting power back in the hands of the people.

The issue that appears to be rising, and please correct me if I'm wrong, is the limited size of transactions each block is allowed, therefore creating higher transfer costs on the blockchain. As well as an enormous amount of electricity to "mine" or compile the blocks.

So, heres my question.. could the creation of blocks and the insane electrical cost per mining operation be solved by having every household equipped with a mining machine that didn't cost much more than your typical computer to run? This thought could be my very limited understanding of this technology.