Yes. if a bank would sign a contract with you then it is valid. I highly doubt that would be the case, the bank needs to borrows the money from someone else. They just merely make the difference in the interest rates. Taking a fixed interest rate would mean that they risk losing money if the money the borrow from somewhere else exceeds 3% in the next 30 years.
>why contract signings are witnessed. In a dispute the witness can testify that you did in fact read, appear to understand, and willingly sign. And this is why online TOS are difficult to enforce
This is not a problem at all. In Common Law jurisdictions (US, UK), contracts do NOT have to be witnessed (with some exceptions like Wills). Contracts that is signed without any witness are perfectly valid. This would apply to your ToS, if it states the laws of US, UK would apply to this contract. All contracts would state the jurisdiction that applies and all (respectable) courts would honor that term.