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I love ice cream. But if I had to eat a billion gallons of it, it would lose its appeal.How do you know? Besides, if you had to eat a billion gallons of it, but over a billion years, I'm pretty sure it would've not lost its appeal at all. It's not "too much" but "too frequent" that takes the joy away.
To counter your example: I watch more TV series than I probably should. What I've learned is that while there's no fun in rewatching the same show just after you finished your first run, rewatching after ~5 years feels almost as if you were watching it for the first time.
I think life is the same. Brains are physical objects with limited capacity for memories and experiences. A million years of life won't be a million years of memories. But it will be a million years' worth of refining your person.
> if we had it in infinite supply, it wouldn't have much value.
Maybe "economic value" under capitalism. But emotional value to the person living.
> I wonder if they have really thought through the consequences.
I know I did. I fail to see a problem with everyone extending their lives indefinitely, past the initial hurdle of rebuilding our economic system to not structurally depend on people dying on schedule, and actually getting space exploration started.
And remember, if you get bored living forever, you could always check out. Right now, we don't even have an option to live long enough to get bored.