I get the impression that they want to ensure people choose meaningful short(ish) URLs, rather than getting random alphanumeric suffixes, because they are invested in the trust placed in the gov.uk domain and it not looking like phishing bullshit. So it makes sense to me that they want to curate the namespace rather than making it either self-service or fully automated.
> `How to request a short URL*
> Submit a new feature request using the support form.
> You’ll need to tell us:
> - the reason you need a short URL
> - the content or page the short URL will link to
> - how your short URL will be used in marketing and promotion
> - the channels you will be using, the number of users who will be targeted
> - what the main message will be in your marketing and communications
> - how many government departments or organisations will promote the short URL