They have started to - they extended the relevant law to close loopholes about “real time” vs “prerecorded” BBC broadcasts, now you need a licence if you use the iPlayer for anything. Which is fair, even if it forced me to get a license again. I expect at some point the law will either get more draconian (by requiring a license for any broadband contract at home) or the BBC will become an actual streaming service like Netflix, with regular subscription (which would be a bit of a disaster, since it would basically mean the end of the BBC as we know it).
Most young people don't watch iPlayer either. It heavily tilted towards older people.
It will only be an issue for people who watch it...
I'm heavily against the license fee, as the majority of content could be delivered commercially. I absolutely hate that i'm paying money towards soaps, cake shows, misses brown boys etc which I will never have an interest watching and get zero value from.
The small amount of state or non commercial stuff it produces could be paid for by tax or a much smaller license fee.
The money i save could be spent a couple of books or rentals instead which I would get value from.
I'm also for getting rid of the licence fee but instead increasing taxes by equal measure and funding it that way. Hopefully enshrine that funding into law. The license fee is just too easy to attack nowadays.
I find the argument for purely commercial a selfish one as public broadcasting provides a lot of public good through educational means. I mean, just tune into The One Show or Spring Watch on an an evening and you'll get what I mean. Plus no ads!