Even so... a standalone mining rig would use dozens or hundreds of those ASICS and consume hundreds of watts, 24/7. If you divide those "extra costs" of the rig (cabinet, PSU, maintenace, etc.) by its hashpower, the rig would probably still be more cost-effective than "parasitic" ASICs in other consumer equipment.
I still cannot see how this hypothetical plan can make economic sense. They may be into mining, but I suspect that appliance-embedded chips is not their plan.
Dividing many chips with a commercial miner with the enclosure/PSU/control board can certainly lower costs but not as low as adding a 10w ASIC chip to a router where it can piggy back off of those items(this must be balanced right as an extra 10w and the extra heat could raise the costs of the router itself with a more powerful transformer and better cooling).
This isn't where the true efficiency gains are realized though. You completely ignored the most important part of gains in efficiency.
Additionally, the whole mining setup, maintenance, troubleshooting, security , liability, and power concerns would be eliminated thus further adding efficiencies that commercial miners couldn't compete with.
Those all amount to sizable costs mostly eliminated by distributing the hashing power to millions of routers and appliances.
Because the issue is not you wasting 10 W; it is someone else using 10 W of your power to his benefit.
I think we mostly agree that using an ASIC for anything but recycling waste heat has a net negative investment from the consumers standpoint compared to them spending those funds directly on bitcoin rather than electricity to mine bitcoin.
The consumer might get a free router (valued at 40 usd), spend twice as much on electricity or an extra 100 USD over 3 years and their 25% share mined would amount to 20-30 dollars of BTC for a net investment loss. This doesn't take into account the value a fairer "rent to own" contract than is currently being offered and doesn't take into account hobbyists that want to support the network, and doesn't take into account the fact that the BTC mined will likely go up in value thus the free router will be profitable for the consumer as long as they don't immediately spend their mined bitcoins.
The bottom line is yes, from an investment perspective it is better to immediately buy bitcoin and a buy a regular router rather than rent to own this one.....but it could definitely become a better investment than buying a regular router and not buying BTC. Thus those regular consumers could still be making a better decision by using this free router than buying a regular one, they just won't be making the best decision.
I would prefer Appliances that used waste heat as there are some real benefits for everyone to be realized there.
