It's NOT just the price of beeswax that controls the price of silent oils. It's the price of beehive chips themselves, and the price of slime oils that really do the most damage. You may notice that beeswax goes up, but this is generally accompanied by (and is the result of) an increase in the price of beehive chips.
I'd say that most mid-level alchemists never buy beeswax; it's too cost-saving to make it yourself. There is a group of people that do nothing but HQ on beeswax and sell it off to higher-level alchemists or powerlevelling crafters for profit, but I don't think most go this route.
This is certainly true of me, and if the number of people I see synthing beeswax in Jeuno and Bastok before immediately following it up with an oil synth is any indication, it's true across the board. You're just missing out on a lot of HQ cost-saving if you don't make the beeswax yourself. Beehive chips, on the other hand, while very easy to get, can take a very long time to farm. This is really what makes beehive chips move so quickly, and is why so many people farm them: a lot more people are buying beehive chips in their raw form than the refined beeswax.
The thing with inflation, particularly when considering consumables, is that everything is so intimately linked. When some lag in supply (or just a few ambitious people) raise the price on one thing, there's a chain reaction on a whole slew of related products that creates inflation across the board.
What I am most frustrated with, personally, is inflation in equipment and spells. I mean, take Sleepga II for example: I started watching the price on it a month or two ago, and it was hovering at around 600k. Not only that, but only one or two copies of the spell would be up every day. Fast forward a few months, and they're going for TWICE that, with 4-8 copies up at a time. There's nothing hurting the supply THERE, and yet, it only takes the careful, gradual price-raising of a few determined people to get the thing to explode.