the point is that vaegir archer got nerfed. So if you have less damage in total you can not take a less damage equipment. alot of vaegir strats still bank on the archers hitting shots, so if you're not able to potentially 1 shot an enemy player with a headshot you're throwing.
Normad bow offers you literally nothing. You get to have additional gold to spend on boots, 2 better packs of arrows and a falcion which is all completly useless. You only need 1 pack of good arrows since you can have all archers glitch it for them. You get everyone a scimi if you know how to do drops, and the leg armor is not needed because you're supposed to be the faction with ranged pressure. So the money you 'gain' for taking a free bow is not really effective. If you buy khergit bow with best helmet you can 1 hit people with headshot. It's weaker now than it was before but it's still possible.
The difference to nids is simply the playstyle. Vaegir archers are supposed to carry, so you need every damage you can get. Sarranid plays more around the axe inf and the mobile cav, their archers have more of a supporting role. If sarranid had a bow available that could 1shot players, they'd use it too.