Free and unlimited electricity? I believe you could mine using older and second-hand hardware if you're lucky to have such an advantage over other mining farms. Because we're talking hypotheticals, you probably could build a partnership with Jihan Wu and tell him to provide the ASICs and you provide the electricity for a 50-50 split on all mined Bitcoins. You're like a quasi-central-bank printing money for free to be distributed.
you only get free electricity at your own house and you have to buy the equipment. no partnering with someone where they send you free equipment. the hardware costs alone might be hard to break even on before the hardware stopped working. that would be your biggest challenge. that and all the noise you generate. so you would have to spend money trying to stop the noise from bothering you and your neighbors. and keep a low profile so that authorities didn't try and stop you from running a commercial operation in a place zoned for residential. it won't be as easy as you think!
Are you arguing against your own hypothetical example? You started the post by saying that,
i'm not even sure that if someone was able to get free unlimited electricity that they would guaranteed to be profitable mining bitcoin.
Which is a laughable claim because if someone truly had "free and unlimited" electricity, that would be a golden opportunity to mine Bitcoin with a very big advantage. Tell Jihan Wu you have a source to free electricity and definitely he'll be paying you a percentage of coins mined to give him access. It's guaranteed profit.