I share your opinion that I prefer to use my personal laptop on work because I own multiple softwares like jetbrains suite, linqpad, vmware workstation, etc. I also like the privacy of saving my password for differents accounts like emails, stackoverflow, etc. Something that I would be reluctant to be saved on a corporate computer.
And I also had the role of a network administrator for multiple years, I understand the need to have full access to the computer, be able to run network polices and protect the network from compromised computers. Personally, depending of the security level required by the business, the company usually cannot block data theft from employee and the dumbest user can get a ransomware.
My personal history is:
I used to work for a company of 50 employees that pay up to 2,000$ for a laptop from a specific dealer. The user were allowed to customized his laptop and pay the gap between the final price and the 2,000$. Then the laptop was amortized on 3 years, if the user quit before 3 years, he could pay the balance to own it. And after 3 years, he could pay 100$ to own it, where the 100$ were investing in a charity fund.
I also work for two companies, one of 150 employees and another of 50 employees were they do not mind that you use your personal laptop as long you it does not get your productivity down, like if you install linux and it crash, it is on your time to fix back the laptop.
And I work for a pharmaceutical company where there is no way a user will bring a personal laptop.
So my conclusion is depending of the employer, talk with them about what can be arranged. During the discussion, I would not use the word bonus because it can raise some issues with coworkers and personally it is more an expense. So after the small talk and stating that I prefer to use a personal computer, I would validate if there is any politic in place that can deny my request then my first offer would be something like: I would like to personally buy a laptop for the job, and after 12 months, I get X$ reimbursed, in 24 months, another Y$, etc. to avoid the company to work to get their money back if I leave after 3 months or I get fired, after purchasing the laptop, I will hand the invoice to the account guy so he can put that in the expense of the company. Also, projecting in 12 months, 24 months, etc. give a look that you want to invest in the company and stay a long time. I think that way it does not look greedy and in long term, you will have a free personal laptop.
I made this move multiple times for hardware, training, etc. Just talking can do a lot, like a got a pluralsight training reimbursed after a number of hours.