I'm a consultant, and have been for 20 years now (except for a 2 year stint as an employee for the benefits and relocation assistance to move my family from Texas to NYC).
At the NYC employment job, I was on a 2 year upgrade cycle being a software developer. Just whatever the current year Dell corpo laptop was. No procurement procedures, just IT got 2 year replacements, our laptops went to the non IT workforce after reimaging.
As a consultant I usually bring my own device, and my laptops are usually WAY more capable since I will run each client on their own VM - makes it easy to delete the client when the contract is up. But I've had one client who did not allow BYOD, and any billed work had to be done on their hardware. That was fine, except that the desktop I was given was already a 12 year old dual core non-hyperthreading CPU that wasn't meant for developers even when it was built. I begged and pleaded for 6+ months for me to either bring in my own hardware they could image now and wipe at the end of the contract, or to please buy me a PC from this decade.
It took 3 years to get the budget approval for a $2000 tower, roughly the equivalent of 15 hours of pay. The thing that finally pushed it over the edge, was that my PC could not handle Teams + Visual Studio at the same time, and manager couldn't handle that he couldn't watch me program.
All of that to say I doubt these non-data-driven organizations are basing these decisions on anything other than micromanagement. Nothing to do with measured or assumed productivity, nothing to do with costs, so all I can think is they have to be a "decision maker" on all aspects.
I never understood why no company I worked at could hire someone just to manage the kitchen instead of paying engineers massive salaries to argue about unloading the dishwasher.
Sounds like your company needs to spend some time working on their onboarding process. Probably more effective than just hoping no one ever needs a new computer.
Whether it's an additional $100/week for base salary or $100/week for overhead Bob is always going to be after another $100/week regardless what his current cost is. If Bob wants to manage the overheads directly (most don't) like salary costs then he probably wants more of a contractor type position.
As to the content of the letter, the 4 paragraphs are supposed to be "these are reasons I think were missed and why it'll cost more to not correct it" not just "I put effort to write 4 paragraphs of stuff" friction alone.
Having run a short stint as an internal IT manager at an IT focused company... it's astounding how many non-standard/out-of-cycle laptop request are actually either basic user error (even for the most brilliant technical employees) or basic IT systems problems (e.g. poorly tested management/security tool changes eating up performance/battery in certain configurations) that a new laptop won't actually solve. E.g. reports of "my battery runs out in 2 hours and my IM is dog slow" but they are on an M1/M2 MacBook Pro and probably wouldn't notice if they got an M1 or M4 MacBook back as their issue isn't actually the hardware. When someone writes an email or ticket explaining why their use case just wasn't accounted for it's generally pretty obvious they really do need something different.
