There are more consumables involved there beyond just reagents and a lot of it was/is proprietary. The machines all had their own consumable physical bits for sequencing as well and getting your hands on those would also be a blocker.
Applied Biosystems Sanger capillary machines (the 37XX series) had polymers that were injected into the capillaries to reflow between runs (the polymer took the place of the physical slab of gel). The capillaries themselves were also consumable and would wear out after so many runs. They were extremely expensive even 20-30 years ago when these were state of the art. You also need the dideoxy dye terminators you read about in the article. The patents on BigDye are expired now (the patents were ABI's principal moat on the Sanger tech and they aggressively used it against competitors like MegaBACE) but it's not like that's a growth market for a vendor trying to make a generic replacement.
Similar with the 454 -- the process would fragment up the DNA into lots of tiny shards, and bind the fragments to microscopic beads. There was a physical flow cell chip that you would flow the beads onto. The chip had microscopic "beehive" cells to hold the beads such that you had a vast array of miniature test tubes running reactions in parallel while the machine imaged the result. These chips were one and done after every sequencer run, and were precision manufactured. They were manufactured by fusing together a bundle of fiber optics and then slicing it like bread, such that you had a glass chip and the space between the fibers became the cells. You'd need the beads, the chips, and the reagents to produce the reactions the machine is looking for.
Without all the reagents and physical necessities these machines are just some really fancy cameras with onboard lasers.
Long story short it's fun to think about getting one of these machines, but unless you use it as a cool looking coffee table that appeals to graying molecular biologists, you're going to be disappointed.