Leaking can be an Indicator of poor alignment. Think of a drill bit not fully centered in a chuck, it defines a more oval movement that expands the packing around the shaft and lets it drip. No amount of tightening will solve an alignment issue without overheating the packing. Though fresh packing is more forgiving, that’s not really a fix to alignment issues, if you have them.
Also, if you tighten packing that has already baked out it’s lubricant and baked the fibers into a hardened state, you can easily score a shaft.
Which is to say that I don’t like tightening packing that is not in a known state of good condition, especially when it’s so easy to change. Only takes a short time to do it and costs little and can be done easily in the water.
If you have dripping beyond normal with fresh packing and a gland that is running too hot, look into your alignment, cutless bearings, prop balance and shaft straightness.