That said, when you're building low-end machines you may find you have a hard time competing with the cheap offerings from big OEMs like Dell
especially if you value your time (and factor in support).
I second this. OEM computers are also fairly quiet, too, especially low-end models. The biggest problem with low-end OEM machines is you often don't know what you're getting as far as motherboard, PSU, graphics brand (if it matters, say you have something that runs better under nVidia drivers) and connectivity.
I know I would hate buying, building, setting up, and configuring 15+ budget machines for an office. That would take a lot of time. You need to count how much time you spend assembling and configuring these machines into the total cost. You might be able to save on the hardware, but add an operating system and there goes your budget. Add the cost of your wage as you spend a couple days building and configuring, and you've gone and spent more company money and don't have any support other than you. It won't look good to your boss.
I know a guy who was outfitting an office with 30 or so machines. He narrowed it down quickly between two OEM machines, ordered one of each through their business line, got them, plugged them in, compared them, and ordered 30 some more of the better model. I think the "worse" model was put up for sale to employees at a discount without support.
Start at hp and dell's business line.