Yes, I find that very annoying, especially from a company like Apple. I have no problem with the free version of the app showing ads, but as long as I'm paying for this service, I expect 0 ads on the service, both for the news and the magazines. It's the only paid service from Apple that displays advertising (except the Apple TV + teasers but it also aims to introduce us to new content so that doesn't bother me).
I'm all for the financial support of the media, but a paid service has to bring benefits and Apple News is not a very good experience in that regard. I suspect, however, that Apple will do nothing in this regard until the service is profitable (and I have a feeling that won't happen in the short term). Maybe they should create an ad free tiers for Apple News (and as a Apple One Premier subscriber, I would expect that this tiers would be included in my bundle).