Indeed. This is one of the few times I carry a rifle with a round chambered. I shot two Sunday morning in the exact same environment you describe. There is no way that either would have hung around had I moved even slightly, let alone rattled a cartridge in to the chamber. One was about 20yds, the other around 50yds. Barely any wind, deadly silent all morning. You could hear a mouse fart.shooting say muntjac in most dense woodland and narrow rides without a chambered round ready (safety on) , i doubt you would get a shot with an empty chamber , unless you found a very dumb one, drawing a bead on them is hard enough as it is .
Same as foxing at night. Soon as the thermal is on and NV focus adjusted and quickly tested on the sticks, a round is then chambered with the safety on.
Where I do dislike having a round up the spout is when moving around with other people or when I am shooting stuff more remotely like medium range pest control. If I can avoid having a rifle ready to fire, I will. Sometimes it just isn't practical though.