Size is treated as a budget lever. It is really a legibility spec, and the two pull in opposite directions.
One inch: conversation distance
Room for one word in a strong weight, and very little else.
Genuinely right for role buttons — VOLUNTEER, GREETER — and wrong for a name and an office.
Two and a quarter: across a room
The default for a reason. A name, a short line and a mark all read comfortably.
This is the size most campaigns should be ordering and the size most under-order.
Three inch: across a hall
A name, an office and a strapline without any of it dropping below readable.
Worth the extra cost the moment the room is bigger than an office.
Six inch: down a rally line
Reads at distance and survives being cropped into a photograph.
Needs a reinforced or locking pin, or it tips forward on soft fabric.
The honest test
Stand where the furthest person will stand and ask whether a name would read from there.
If it would not, the cheaper button has cost you the whole order.