No the crossbow is less versatile, and isnt 4x as powerful as a bow as the reload time.
What you say is that all racing cars should have an automatic gearbox because thats the newest, most advanced technology, it is but it doesnt mean its better if you can use the other one right its better.
In TW also the firing rate for crossbows is unrealistic.
You know the crossbow came from china? Before it was improved in europe it went over many lands, and when europeans fought in areas using bows, why didnt they start using crossbows? The places in the east were actually more tchnologically advanced that europe.
Can you tell me why english longbowmen always beat french crossbowmen?

Early guns vs Crossbows: I think crossbows would win due to greater range.
Early guns vs Archers: Archers should win due to greater firing rate and range