I'm not opposed to having specific anti-immunity effects written into an adventure or monster when the situation really warrants it. If it's really a once-in-a-millennium elder god arising type of situation, and fear is an important element of its design, then sure, having "this even affects creatures that normally can't be frightened" in its frighten ability might be a good idea. I do, however, oppose the idea that negating player abilities should be routine, or is even necessary in tier 3/tier 4 play.
Part of the challenge for high level adventure design is that they should adapt to high level character capabilities; the fun of playing high level characters is that you have access to all these tools and abilities that you never had at lower levels. High level play shouldn't devolve down to feeling just like low level play, but with bigger numbers; players should feel like they have a lot more power and agency at high levels, and if sometimes that allows them to circumvent what would otherwise be a difficult encounter, so be it.
Phlan1-3 (tier 3) is an example of a high level adventure that fails to rise to the challenge. Much of the adventure could have been solved by the players casting spells like Scrying and Teleport (disclaimer: I did not read that adventure, I only played it), which would cut away a large portion of the adventure. Worse yet, the adventure suggests that wilderness travel and survival should be a significant challenge for the characters, which is laughable for characters that can potentially cast spells like Mordenkainen's Magnificent Mansion. It felt like a tier 1 adventure scaled up for tier 3, which just doesn't work. And you shouldn't try to fix an adventure like this by taking away player abilities until the challenges become challenging; at that point, why even bother playing tier 3? The way to write high level adventures isn't to say no until the same low level content becomes challenging again.
DDEX3-16 (tier 3), on the other hand, shows the right way to write high level adventures. It's an adventure where you can use your high level awesome abilities, but no one spell is just going to solve everything unilaterally. There are a lot of challenging encounters, and you might be able to defeat one or two of them with your awesome trick, but there's more where that came from, and you're time constrained enough that you probably can't spam your trick every fight. The challenges are epic and feel nothing like what you'd see at lower levels.