Which brings up a whole other long drawn out version of the same discussion. What's appropriate for a source for D&D? Which is already a subthread here. But, like most "discussions" about this kind of thing, people put their goals first so want a curated list of sources that they think are "appropriate" because those sources reinforce their preferences for the game.
There's a whole lot of assumptions you're making in that quote.
The "problematic design" is not just attack cantrips. And it's questionable if that even is problematic design. If martials were boosted to be even roughly on par with casters, cantrips wouldn't matter. If martials are forced to stay lame and casters brought low, then yes, cantrips are problematic. I don't buy that line of reasoning. The best fix, for me, is to buff martials. And to minorly tweak casters. As I said up thread, splitting off non-combat spells into rituals would make balancing what remains simple. Giving everyone access to rituals would then close the majority of the gap between martials and casters.
But, it's worth pointing out that yes, a few of the anime and manga I pointed to do, in fact, have the equivalent to at-will cantrips. The most glaring one is Rudeus from Mushoku Tensei. And though I'm only one the second light novel, I feel confident that a few of his students will get to the point of also having at-will attack cantrips. It's also a great source for boosted martials. Ghislaine, Paul, the Sword Gods, etc. They would all be fantastic templates for proper martials.
And to that point, I mentioned those anime, manga, etc not as a reference point to show at-will cantrips. That's an assumption you made or a bit of us talking past each other. I've mentioned them in the thread repeatedly as an example of what younger fans see and will likely expect as martial characters to contrast that with the the older fans who are still pointing to Appendix N and refusing to let martials be anything more than a mook with a few extra hit points.