It would significantly weaken the rise of cities, which heavily relied on crossbow equipped citizen militia for defense purposes in the high middle ages. To become a decent bowman you have to regularly train from your youth onwards (that's the reason why any other sports were prohibited for the common people in medieval England), for a crossbow a few hours will do. According to tradition King Richard the Lionheart was shot by a french castle's kitchen aide, who had come to the besieged castle's ramparts carrying rations for the defenders and when he spotted the enemy leader riding below picked up a crossbow and took a lucky shot (well, not so lucky for him since he was boiled to death in his own cauldron after the enraged English besiegers took the castle even though King Richard had pardonned the man before succumbing to the injuries caused by the crossbow bolt).
Of course, the burghers had been using crossbows but successful city and/or peasant militias, Flemish and Swiss, had been relying much more upon the attack of mass infantry formations armed with the pikes, halberds and other types of the pole arms.
Legendary kitchen aid was within a
castle, not a city and Richard himself widely used the crossbow men both in Europe and on the crusade. Not sure up to which degree Richard’s army during that siege was “English”: even disregarding the fact that Richard himself was French and did not speak English, order to execute a crossbowman had been given by Mercadier, a leader of the Brabant mercenaries on Richard’s service, who took castle by storm.
