Ugh, I'm really ready for this arc to be over. I don't like time travel stuff -- especially so when it isn't the central conceit of the series so only part of the plot is built around it. The only way this ends is either the future is completely unchanged which makes any threats presented impotent, or the future gets changed which makes all the time we've spent before the time travel weaker because it gets overwritten. We already had a method to explore the past in the form of Frieren's and other people's memories of them. Was going to the past for an extended period of time really necessary?
It also makes it feel like this series is all about Frieren. The framing from the start of the series was that Frieren's old journey was over but she would meet new people and make new connections. Now we're just forgoing all those new people to dive deeper on her and the past.
If it makes you feel any better, we already know what almost certainly happens, in that Frieren has presumably already gone back in time at least once in the past the first time she analyzed the monument, meaning we know the aftereffect of the spell, and because the spell was on the monument at the start of the arc, the events in the arc had already happened before they arrived, meaning it was set in stone to happen anyway. This means that we can pretty reasonably assume that the arc will end with Frieren returning to the present with a blurry memory of her time travelling, but will still have the feeling of closeness to the Hero's Party that was strengthened by her present self and understanding spending time with them.
Another possibility is that the monument temporarily replaces past Frieren with present Frieren, so the blurry memory was actually past Frieren not having been conscious while present Frieren was in control, which also explains why present Frieren seems to not remember this at all despite the fact it had to had already happened (as past Frieren never knew, so our Frieren wouldn't know)
Of course, neither explanation explains why or how Frieren could spend time analyzing the monument and succeed when we know our Frieren has not, creating confusion in what's going on (as how could Frieren analyze a monument she hasn't analyzed). A possibility that does explain this, however, is that future Frieren, after the end of the story, analyzed the monument and figured out how it works, and then went to a time between the two incidents to carve the name of the spell onto the monument, with Frieren not remembering it because of the effects of the monument on memory.
Finally, while it isn't necessary, time travel offers us an entirely new way to see Frieren's adventure, as tales and recollections of the past are inherently recollections, it is Frieren looking back on the journey. This allows us to understand how Frieren feels towards the past, but it is limited in that they can only be introduced naturally if they have some bearing on the active storyline. Time travel, on the other hand, lets us focus on just the past without how it affects the present, which can give us a new avenue to explore Frieren's connections and how she has changed in the past 80 years, while also giving us a way to explore Frieren's motivations and why she still journey's in the present as well as how she feels towards the present.