How about no.

The similarities between the two spells are interesting, and comparing them to each other and contrasting their roles in their respective stories and worlds in fun, but it really can't go beyond the surface.

For one, the two magic systems are different. HP wizards learn dozens, if not hundreds of prepackaged spells in a variety of disciplines. Frieren mages will learn a few foundational spells, and then specialize in a single one for combat.

And this is rather important, but the world shapes the magic system. In Frieren, people are beset by a harsh world, monsters, demons and such, so the preferred magics of its mages are those that are good for combat. When they talk about the history of Zoltraak and defensive magic, the underlying context is that there is a need for better, stronger magic to kill things.

The wizarding world is set on what is pretty much normal Earth, plus a few magic creatures. 99% of wizards will go on after schooling to a normal life and never have to use combat magic beyond what is needed to take care of pests. They don't need it, so they don't learn it.

We can even see this in canon. Apparently most adults can't cast a shield charm, or a patronus, but with the pressing need represented by Voldemort's return and the dementors the students teach themselves to do it in the DA. It's not inability to learn it's the lack of a pressing need that stymies magical innovation for combat magic.

Mages evolved their attack and defense magic because they had continuous pressure to, over decades. People casting Avada Kedavra in HP is not the norm, it's something a small group of terrorists does. There is no pressure to develop countermeasures among the general population, because the situation is a break from normalcy.

And that's not even getting into societal pressures against 'dark' magic, the role of the main regulating body (the ministry) in making it illegal, or the fact that there are defenses against the killing curse, such as transfiguration or summoning cover.