Putting aside how terrible everything in the world would be considering that most of our energy comes from non-renewable sources, mining would continue to be almost equally profitable to now.
The difficulty naturally adjusts to make mining barely profitable - if it's unprofitable, the number of miners decreases and the difficulty adjusts to make it profitable again. Therefore, if electricity were free, far more miners and far more computing power would be dedicated to the network for essentially no reason and it would be a giant vacuum for machinery all over the world (as it already is, simply because of how limitless the current PoW system is), which would eventually even out and only rise along with Moore's Law.
In a hypothetical (and impossible) world where electricity is free and unlimited everywhere, there would be no incentive to sell miners since they would always be making profit. The supply of used, cheap miners would then be virtually non existent and just getting into the game ends up being a big investment. The hashrate ends up being mostly owned by a few rich investors, not a very good outcome.
In a slightly more realistic world where electricity is free everywhere (but not unlimited), nobody would sell older miners until the limits are reached and they are forced to remove the least efficient ones in order to free up capacity for new miners. The supply of used miners would be scarce and the demand very high, again keeping most of the hashrate with the rich investors, just a little more spread out.
And in the real world we actually have now, the mix of areas with electricity costs ranging from relatively high to "free" makes for a good "trickle down" market for miners. Maybe it's a good thing new miners are noisy and expensive so those with free electricity don't kill the profits of those who don't?
