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.
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.