This isn't a bad idea in terms of gameplay, but in terms of the underlying technology, "mighty crossbows" are
vastly more sophisticated than
any composite longbow and were developed more than a few millennia after those simple devices were first created.
The difference is not in the recurve of the bows. Woods, horn and sinews were used to make them and their construction techniques were VERY similar. The drawstring on the crossbow was ultimately very different, but that is not critical on its own, either. (Though ultimately, braided wire is extremely sophisticated metallurgy.)
The BIG difference is in the trigger mechanism. One had one; the other did not.
"Mighty crossbow" trigger mechanisms were the most sophisticated examples of engineering in the entire Medieval and early Renaissance world.
If you are wondering how the interplay of these crossbows "might" impact upon your gameworld, keep this in mind in terms of how our "real world" experience developed:
When it came to crossbows, the REAL high-technology involved went beyond the pull-weight of the bow. What was necessary to make it all work were increasingly sophisticated fine metallurgy skills and techniques that could make a small clasp which was strong enough to grasp and hold the drawn string and yet be able to release it smoothly. The stronger the draw weight, the more sophisticated the trigger had to be.
This was
not a small point and was, in fact, THE high-tech of the early to mid-renaissance. There was a constant interplay between the metallurgists who were good enough to make these crossbow triggers and the armourers who tried to defeat them. While gunpowder ultimately overtook this process between crossbows and armour and made that competition moot, the technology in crossbows triggers had IMMEDIATE application and migrated to other weapon and non-weapon uses.
Because the trigger mechanisms were very similar, the metallurgists who worked on crossbows were the same artisans who developed all sophisticated triggers for Renaissance musketry. More importantly, as they mastered all of these skills, they became highly proficient in using small springs and tiny gears -- and that knowledge DIRECTLY lead to the manufacture of clocks and watches.
There is a REASON that "Swiss Watches" became the gold standard through modern Europe. The artisans who became Swiss Clock makers were the same artisans who developed the triggers for "mighty crossbows". Those weapon makers ultimately moved to Switzerland (and some to Bavaria) to escape taxation and being pressed into service by various and sundry of the nobility of France and northern Italy. Most of those soon to be "Swiss Clock Makers" spent most of their time supplying the Italian city states and their mercenary armies with increasingly stronger crossbows.
Because that same technology then permitted the creation of accurate time pieces, that in turn had a profound effect on the Enlightenment and permitted accurate time to be recorded and used in scientific experiments, facilitating the Scientific Revolution and permitting, ultimately, a way to fix longitude as well in global navigation.
That same technology also directly lead to the earliest mechanized looms for the production of cloth during the early Industrial Revolution.
It all came DIRECTLY from the "mighty crossbow" and the sophisticated triggers required to make them work.
It may seem like a simple analogous weapon to an existing composite strength bow, but you are, in fact, messing with
highly sophisticated technology that is the technological basis for all of Early Modern Europe which laid the foundation for the modern world.
Just sayin