I'll not weigh in on the "why" or the "should", but I can help with the "how". I'm what you might call a serial entrepreneur. I've owned a few companies and consulted for several startups. If someone came up to me and asked how this could work, here's how I'd go about it:
First off, it would help to be based in a state that allows LLCs. Most do, but not all. Additionally, one that doesn't have state income tax would be preferential. Set up a simple LLC to keep track of the taxes and keep everything above board. Filing fees and required documents vary by state. From memory, I think it's $50 here in CO, and aside from required internal documents, which a lot of companies don't actually ever really seem to get around to drafting, I want to say it's really just a single form and a short one at that. File at the federal level as well.
The individual doing the leg work here will be required to file income and self employment taxes at the federal level (I'm not going into state stuff since it's different everywhere), which need to be paid in quarterly installments. This can be done online, and it's pretty simple and straight forward through the IRS's e-file system. Ignoring state income tax, at the $60K/year rate I saw above and with no significant deductions I want to say you're looking at ~25% all in.
If anyone is worried about tax liabilities due to orders out when fiscal years end, just keep the accounting straight and trust that it'll net out in that the amount you pay extra one year comes back the next more or less. If it's a huge concern, go on holiday for whatever lead time works out to be at the end of your fiscal year. Your fiscal year doesn't have to end 12/31. So if xmas is a major buy time, have the FYE in March so the Helter Skelter has died down a bit.
Keep accurate records or spreadsheets or what have you, and if you really want to get serious Quickbooks is only about $30/month. Play it smart and don't take cash or checks (who would in 2016?), and your CC/PayPal statements will handle a lot of the lifting for you (most have Excel and QB exports that make this super painless).
Logistically, work with the GH moderators to rehash how ICs/GBs work and get things streamlined such that this 'caretaker' doesn't have to handle every single post in every single IC/GB. Additionally, keycap set-oriented GBs would need to be required to fit in whatever limitations this particular manufacturer has. That would honestly take care of the lions' share of the effort right there... This way, the 'caretaker' only handles completed GBs, and can handle intermediary legwork that sounds like this particular supplier needs and can't handle themselves. Once a GB is completed, the 'caretaker' submits an order for such-and-such keycap sets in such-and-such colors and configurations. This could even be done on a weekly basis to further mitigate workload. I'm not sure how these keycap sets arrive, but if it's just a loose pile of plastic you'll need to sort it out, that would be the biggest time consumer. If they come pre-sorted/setted and all you're doing is really handling shipping, labels are easy to print and the hard part simply becomes keeping track of which stickers go on which boxes (sharpies work wonders here). It's also easy to schedule pickups with whatever shipper is preferable. Have them come once a week and pick up your stack o' boxes.
Once you've gone through the initial entity formation and get in the right habits, you're looking at something like one day a week's worth of actual work if you're organized.