You will never break a line of 3lb BS line with a normal float rod.
Infact you may not even be able to break 1lb BS line with a float rod!
So, irrespective of the weight of the fish on the hook, if it stays attached you cannot break the line by pulling on it, because the rod will bend and break first.
The problem starts with the knots we use, most being somewhere between 50-60% of the BS of the line.
Factor in nylon mono being 5-12% air and the effects of it being soaked in water for a few hours and we are using a unmeasurable product.
(Please note that the IGFA soak mono before carrying put their line class record claims).
Then you can add nicks and scrapes sustained during a days fishing, the effects of exposure to sunlight and you can see why we use 3lb mono to catch a 6oz fish..
Margins of safety is a better way to describe it.