Its not that such entities that will correctly handle the e-waste don't exist, its that the company doesn't want to pay to have it donem esp when storage is cheap, let those containers of old laptops and towers be someone else's (budgetary) problem.
This is the relevant bit. It's cheaper just to pile the old computers in storage vs doing something about it.
Companies leaving their waste as someone else's problem to deal with is a common occurrence (heck, even before they go bankrupt), and in many cases they would never have existed in the first place if they had to pay for all of it, for instance :
https://www.desmog.com/2019/12/20/fracking-oil-gas-bankruptc...
(Note also that there are funds set aside for cleanup, but they are typically woefully insufficient.)
How to prevent companies that are a net negative for society from existing remains an unsolved problem.
(Aside of course from disallowing companies altogether, I wonder when is the point that the limited liability company as a concept is a net negative to society ? Could it be in the past already ? Of course comes the question of whether any alternative can have a positive contribution, in a context of overshoot...)
Now that storage is often an indistinct chip on the motherboard, I wonder how that works.
In my country, there are specialist e-waste disposal companies large IT organisations can hire, which guarantee to remove and shred the hard drives before recycling the rest.