I thought 'digs' meant 'rented room or flat', I've never heard of this term. I think charging over 18s some rent is fine but that's a different thing entirely.
What your DH describes seems to relate to a situation where the family is struggling and there is an expectation that every member will work as soon as they can in order to pull their weight (so more than likely go into FT work rather than further or higher education).
If you are not struggling, have not brought your children up with this expectation of needing to contribute to family finances, can afford to meet their needs and are in fact happy to support them through their post-16 education, it makes no sense. It is a disincentive for them to work, as the alternative is they don't bother and everything is paid for anyway.
The incentive to work is ability to pay for extra luxuries and a degree of financial independence. That's true on all or half their earnings, except that they may well feel it's not worth the effort for half.
Morally, if you take some of their money without needing it, you free up some of your household budget, so you can spend more on luxuries for you. What's the justification for that? This concept only works in households where there are no or few luxuries.
I took on a newspaper round at 13, then babysiting and waitressing until 18. I wouldn't have done any of those jobs for half the wage as, aside from evening babysitting, they were hard work. I valued the financial independence and, my pocket money did stop, not as a calculated idea of 'contribution', just because 50p a week seemed irrelevant compared to £4.50 and I think I was happy with that, as I felt more grown up. I did then get a clothing allowance at 16.