I tend to marine grease any bearings now.
Pro/Con’s
Old threadded headsets need the whole thing replacing if the cups get pitted – pita if you don’t have tools. Cheap unless you have the old threadded headsets with cartridge bearings – no-one makes the bearings – Shimano 1″ and 1 1/8 I’m looking at you Shimano (although they are strippable and serviceable with non caged balls if needed).
Cartridge bearings (external and integrated), then £20-£30 on bearings, usually just the lower needs doing.
I consider them service items now – lower bearings need doing more often. I’ll strip and refill with marine grease – resists the water.
I find water can get down from above and settle at the bottom of the headset, so grease it all.