That would work, but it's not how to works apparently. According to this veritasium video, it's because of "negative pressure" aka tension.
https://www.youtube.com/watch?v=BickMFHAZR0
I recommend watching, I think it's one of the best veritasium Dereck has ever produced.
I suppose that’s not particularly relevant for more recent old growth tall trees that seem to have got by fine in a colder Earth.
But it’s easy to imagine a warmer, wetter, Earth with higher atmospheric CO2 concentrations being more conducive to taller tree growth.
On the other hand, I probably don’t really know what I’m talking about, not my area of expertise.