Assumptions about the company are driven by Ripley's paranoia, but as Bishop showing up after Ripley thought he abandoned her proved, it's all about 'a certain point of view'.
Burke was a greedy f**k who had clambered up the corporate ladder by looking out for number one. He wasn't necessarily the best at it, but had the capacity to be ruthless if he needed to be.
He cut corners. He tried to get sole patent. He wanted to get set up for life - just as he explains to Ripley. But his arrogance gets the better of him. He assumes others think in the same way, probably because many of those he works with
do think like that. How else does one explain him thinking Ripley might actually respond positively to his offer?

But the company, itself, isn't an evil entity. It's completely, utterly indifferent. It's Google writ large. It doesn't care. It exists to make profit, because it's basically an apex predator of the corporate world.
Here's a relevant example:
https://twitter.com/stevekrenzel/status/1589700721121058817He's someone who worked at Twitter and goes over how the hierarchy tried to get him to do something extremely unethical. They were doing it, not to be deliberately evil, but because they thought it would give them a secret edge - which it would have, but at the cost of also being wide open to potential abuse.
The same thing's happening at Weyland-Yutani. The company, itself, doesn't care. The Alien is, potentially, very profitable, so, they want it. Now, if the right person got ahold of the Alien? Someone competent? A
not-Burke, if you will.
Well, we know from '
Alien Resurrection' that the creatures
do have some great exploitable traits. They mentioned new alloys and vaccines. Those are valid results! Now, Wren talks about potentially using it for "urban pacification," but that'd be ridiculous and it's classic Joss Whedon comic book fantasy. What would be the point in unleashing Aliens in the midst of a riot? You could get the same effects by shooting automatic grenade launchers - and a lot quicker.
But the company is like the USM and it has at least a reputation for cutting corners. I mean, even the USM used illegally procured human hosts. Why? There was literally no need! It was for shock factor in the script. Realistically, it would probably be more like the '
Genocide' comic portrayed, where an artificially vat-grown 'host' would suffice.
So, let's assume Weyland-Yutani get ahold of them and are even able to breed them in sufficient numbers... What happens?
Well, they exploit them. They use them up and figure out a way to get those desirable elements from synthetic manufacture. Once they do that? Alien is surplus to requirements. No need to keep them.
And the company wouldn't care. They'd get what they want and just move on.
This is the problem the EU basically has. It's written, largely, by people who feel a need to depict the company, itself, as evil for evil's sake. Some of them try to think up things they'd do with the Alien, itself, but... What is the Alien? It's a ruthlessly opportunistic parasite. It doesn't make a very good weapon, unless it's up against nothing but unarmed colonists. It isn't capable of doing anything a private military force can't already do much quicker and more efficiently.
Which is why the company wouldn't care. They
individuals who run specific departments will vary in how psychopathic they are. One guy might be like Burke and be willing to do whatever it takes. Another would find Burke's activities reprehensible. Most would probably just regard what he did as wasteful and enormously counter-productive.
If he'd gone about things in the proper way, he wouldn't have got his personal patents, but the company would have likely set up a secret base around the derelict, spent years/decades analysing the technology, used droids to extract the eggs and place them under carefully controlled laboratory conditions.
And all would be well. But where's the story in that? There wouldn't be one!

But the company wouldn't care, one way or another. They want
products. Whether the relevant department head in charge of gaining control of those products is a predatory psychopath, is another matter, but they could just as easily be the complete opposite - or even be a small committee made up of several people, all with their own personalities.