The classical definition of consideration is set out in Currie v Misa as:
"some right, interest, profit, or benefit accruing to the one party, or some forbearance, detriment, loss, or responsibility, given, suffered, or undertaken by the other."
In england-and-wales the general consensus seems to be, as noted in Contract Law: Text Cases and Materials (11th edn) [2024], that courts will almost never find there to be no consideration. The book notes that academics generally believe that the doctrine of consideration exists for historical reasons and would not be a requirement if allowed to "start over".
Indeed, Lord Steyn himself said:
"Once a serious intention to enter into legal relations and a concluded agreement is demonstrated ... there is virtually a presumption of consideration which will almost invariably prevail"
In practice, this means that a contract will rarely fail solely due to a lack of consideration anymore. A contract that fails on this basis will likely fail on other points. Where consideration is the only factor, the courts have shown significant judicial creativity to allow controversial means of consideration to be permitted.
In the context of your question, this means that the courts would likely find there to be valid consideration in this case. Two examples of judicial creativity are the following:
- Even though Alice is not paying, her promise to enrol and participate in the course could be consideration.
- The contract is interpreted to be between 1) Bobs University, and 2) (jointly) Alice + the government. Here the government is no longer a third party and is able to pay the consideration on both of their behalves
On this (or a similar basis), the courts are likely to find that there is a valid and enforceable contract. More generally, the requirement for consideration is usually regarded as academic when looked at in practice.
Although this answer is written in the context of E&W, this reason follows through to new-zealand fairly easily as another common law jurisdiction. For example, in Antons Trawling Co Ltd v Smith [2003], the Court of Appeal of New Zealand held that contractual variations could be made without any valid consideration (going even further than E&W in this regard).