Interesting history! Thanks for the explanations. Regarding the woman being owed £100 or the parked car etc., I feel like in an ideal world that kind of thing should be easy to resolve 'correctly' without involving "contracts" at all (which in my mind should be defined more narrowly, more on that below) -- e.g., I (1) would have different requirements for enforcing things in the favor of the same party who wrote the terms rather than against them, and (2) feel you can resolve these situations by lumping them into other categories than contracts (if you could define contract law to accommodate this), like maybe "false advertising", "bet", "fraud", "sale"/"purchase", "unfair competition", etc.
The reason is that I feel a "contract" should be limited to conscious agreements on both sides -- and currently, we have contracts where neither is aware of both (one side doesn't know existence, other side either doesn't realize it's a contract or doesn't know all the terms), which is rather... nuts. Why do I think it should be limited to these situations? For a number of orthogonal reasons:
[1] Rules in a contracts are "open" sets rather than closed, so to speak. With something like false advertising, the rules are already set, and (at least in theory) their consequences have been brought up by various parties and taken into consideration by the government, and people just have to play by them. But with a "contract", you're letting arbitrary people make more or less arbitrary rules. Well, it seems natural that if you want to enter the rulemaking business -- society should have a reasonably high bar for that, since after all you intend to later be able to use the same society's government/legal system to enforce your more or less arbitrarily powerful terms against the other party. Requiring that all parties at least be consciously involved and aware of the rules really seems like the least you could do to demonstrate you should be making rules for someone else to play by.
[2] I think the traditional sit-down/signing/handshake is the image most people traditionally think of when they hear "contract", where both parties are aware of its existence and terms, (rather than, say, a parking lot or a ticket purchase). So treating it like this just makes the law reflect the reality that people would expect, which seems like a good thing on its own.
[3] There's an inherent power imbalance simply by virtue of the fact that, quite often, one side has to spend 1/#contracts'th the amount of resources per contract compared to the other, since once you write the contract for the first person then there's next to zero cost for everyone else -- and hence it encourages you to make the terms long and unfair, so that it's not worth it to the other side to challenge them. Really, I see it as something that should be practically a moral duty: if you want to have a fair "contract", with all the force of law behind it, you have to set both parties on equal footing, having humans involved on both sides and aware of everything is really the least both parties can do. It may seem radical... but can you just imagine if every company that wanted to put unfair terms in its contract had to have a representative explicitly tell the average Joe about this and have him consent to it explicitly (instead of just giving him N sheets of paper and having him sign in large blocks he obviously won't read)? People would get so upset and/or would have so much of their time wasted all the time, which introduces inherent friction and negative feedback into this route. It's just so much harder to spend 30 minutes explaining to someone that they have to sacrifice two arms and a leg if they buy your software than to just give them 10 sheets of paper to read while you move on to the next customer.
So these are why I'm not such a huge fan of lumping everything into the "contract" category... they often just seem wrong on so many of these levels.