The number of people who sit in front of an auctioneer all day on a particular realm is tiny. You can see for yourself. That is not the capacity issue.
Possibly the region-wide commodities AH backend is where the problems are occurring – if they are even load-related! – as it has auctions from ~80 servers, and this is an active time for new expansion commodities. But it’s completely on Blizzard if there are scaling issues here.
Personally, I think there are problems that have very little to do with the activity.
But the number of people sitting around sniping is lost in the noise.
Every “put” (as opposed to query) action that TSM takes requires a UI input – a click or mouse wheel or whatever. Every API is throttled for every user no matter whether that user is using an addon or just clicking as fast as they can.
In general, TSM can post or buy 1-2 auctions per second, which is not fast. By way of comparison, Blizzard’s internet game data API will return an entire AH scan containing as many as 100,000s of auctions in a few seconds and will do it for you as often as you can call it (as the limit is many 1000s of calls per hour, even to that API).
And remember, each post or buy requires a UI input. Click, wheel, keypress, whatever.