Chrome and FF are both *far* too heavyweight -- most especially Chrome, but even FF needs much more memory than a PW1 has in total (256MiB) let alone the amount it has available after the framework has launched (~90MiB). Plus there is of course no swap and the CPU is only 32-bit anyway so there's no hope of >4GiB of address space.
Even more recent readers like the PW3, Voyage and Oasis only have 512MiB RAM. This is the embedded realm: multi-gigabytes of RAM and copious swap aren't available here, and big desktop-ready browsers aren't really going to fly.
(This is at least in part for power reasons: dynamic RAM is a power hog, and it never stops drawing power as long as the machine is on, so the less of it you have, the less power you need. Tablets don't have the same constraint because their backlit colour LCD screens consume far more power than even the hungriest RAM loadout, but one of the selling points of e-ink Kindles is that their batteries last so long you can forget about recharging for days or even weeks on end, so power consumption minimization is still important there. Indeed they're exploiting this in new ways of late, with the Oasis split battery model: a tablet with the same amount of battery as the Oasis in-device battery would probably run out of power in half an hour!)
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