Yes, you needed a licence because analogue broadcast meant everyone who was capable of receiving any TV picture was capable of receiving BBC.
Analogue switch off meant that everyone who wanted to watch TV was going to have to acquire another means of delivery, whether that was via a subscription service, or just some means of receiving the Freeview service.
When the Charter was reviewed during the period of the analogue switch-off, the subscription service providers argued that as they would be able to tailor packages to the desires of their customers, their customers should have the right to 'opt out' and choose to receive a digital package that did not include the BBC, thereby rendering themselves incapable of receiving BBC in the first place and simultaneously removing their obligation to pay for a licence.
It was precisely to pre-empt this and protect the BBC's source of licence-derived income that Cameron's government amended the licence act to mandate that all providers of digital 'terrestrial' broadcast, whether that is subscription or otherwise, must include BBC in every single one of their packages, meaning that anyone in the UK who receives any service that supplies the formerly 'terrestrial' service also receives BBC and is therefore obliged to pay for a licence, hence why you can not legally watch live ITV, C4, C5, Sky One, Sky News, etc in the UK without a licence even though the licencing act only applies to BBC services.
If the act had not been amended, then Sky, Virgin packages etc would be in the same situation that currently applies to Netflix, Disney+, and so on, in that they would have been able to offer packages that did not include live BBC broadcasts, and therefore be free of the obligation on the customer to also hold a TV licence.