You can see why this is attractive to Government. Almost all AAB-and-above students already enter HE, so by uncapping them at the individual institutional level they are unlikely to see more numbers in the sector overall; therefore removing caps at this level is unlikely to cost Government any money. Moreover shifting the balance so that elite institutions have to compete with each other for applicants, instead of applicants having to compete for places as they do at the moment, would also be desirable for Government.
For the elite institutions, though, this would be a very undesirable development. Firstly most elite institutions wouldn't want their Undergraduate provision to grow at the expense of postgraduate and research, because this would distort their mission. So they would see a real threat of losing numbers, but not an attractive opportunity to gain numbers. Secondly, even if some institutions decided to go for this growth opportunity, they would face very significant legal risks.
Remember that many applicants have no A-level tariff, or have tariff as just a part of their qualifications. These could be older applicants who have done Access courses, or foreign applicants (French people, let's say): they are not necessarily poorly qualified applicants and might well meet the institution's criteria for an offer.
The Equality Challenge Unit gives us a helpful definition of indirect discrimination.
Indirect discrimination occurs when a provision, criterion or practice is neutral on the face of it, but its impact particularly disadvantages people with a protected characteristic, unless the person applying the provision can justify it as a proportionate means of achieving a legitimate aim. Ultimately, if tested, it will be for a court of law or tribunal to determine what is justifiable.
So to give a place to an applicant with AAB-level tariff points, whilst refusing another to a highly qualified applicant from France, or an older applicant, is likely to be unlawful indirect discrimination on the grounds of race or age especially where the institution cannot show that this discrimination is down to the exercise of academic judgement about the precise qualifications required for the course (e.g. if you have admitted other French people onto your remaining capped numbers). Now as an elite institution you might be able to afford an outstanding lawyer who could argue that maximising your revenue was a 'legitimate aim' in the meaning of the Equality Act 2010, but why would you risk the cost of going to law?
Therefore I would expect to see very few or no elite institutions taking the line that their courses were full except to applicants with tariff over AAB.