True or false-platinum is nearly unobtainable without significant damage?

Damage is cumulative. Lightest blonde is not possible without damage on hair that has already been processed several times. There is only so much each hair can take!
Highlights are often done with much higher peroxide levels because they need to get to the desired shade in one go (you can't go back and spot bleach after the foils have been removed, especially if they are fine highlights) and it is an off the scalp method. So your hair that had been highlighted was pretty much at its limit already. You said your highlights were covering the majority of your hair, which means some of it would have been bleached more than once too.
The secret to healthy blonde hair is to only bleach once if possible. If more than one bleach is necessary, then the lowest volume peroxide for the shortest amount of time is the safest way.
We have to take into consideration what our hair has been through when making colour decisions, especially if it is long.
Your mistake was bleaching already fragile hair twice in five days. You have been lucky, most people would either have mushy chewing gum hair or a chemical haircut from doing that.
Bleach is damaging, there is no way around that. The only solution is to strand test, and if the strand shows damage (which may take several weeks to show) do not proceed. Hair that is already close to it's limit needs cutting off before any further processing to the hair.
So is it possible to have healthy platinum hair, absolutely.
Is it possible to achieve this on hair that is long (old) and previously heavily processed, no.

As my hair grows out and I cut off the old hair, and only bleach the virgin roots, will the condition improve and the color become more pure of a platinum? The roots are the right color, they also are in better condition than the rest of my hair because they only had one round of bleach applied.

My stylist told me it would all blend..it all looks blonde but it isn't all bleach blonde like how I wanted. I wish she had been more honest, because then I would have just changed up my highlights.

Absolutely, once you cut the old highlights off, your hair should feel much better. Hair that has only been bleached once and is looked after can definitely be healthy.
If I remember rightly you posted that your stylist was reluctant to do an all over bleach, but you insisted on it.

Absolutely, once you cut the old highlights off, your hair should feel much better. Hair that has only been bleached once and is looked after can definitely be healthy.
If I remember rightly you posted that your stylist was reluctant to do an all over bleach, but you insisted on it.

Yup. I just wish she had told me it wouldn't be platinum. I did insist though. I wanted to be really blonde