I am not telling you, I am merely stating a few historical facts.
Medieval illustrations were often known for gross inaccuracies. They wereusually done by artists with no first hand knowledge of their subject.
Even if illustration is accurate, the Normans used Norse style wooden short bows, not long bows.
On the mounted infantry;
The charging lance was not invented until the 11th-12th century so cavalry did not have shock value before that and was used mainly for skirmishing and trampling scattered units.
Because of that the usage of mounted infantry was common at the time since well equipped soldiers were far better trained in fighting as a cohesive infantry unit then a cavalry unit(including the nobles).
This of course, completely ended once the charging knights took the lance as their primary weapon and cavalry tactics improved to include anyone that could afford a horse.
Because of that, all soldiers that were on horseback were used almost exclusively as cavalry units unless the battle situation required the complete dismounting and fighting on foot.
Thus, the usage of mounted infantry was obsolete and useless since a mounted soldier could be far more useful considering the improvements in cavalry usage on the battlefield.
"That would have made them Mounted Infantry. Who could keep up with the cavalry on the Strategic level."
What does this even mean?
What strategic level?
The cavalry moved alongside the infantry right until the charge that lasted about 20-40 seconds until they bashed into the enemy line, what use would longbowmen be following around a cavalry unit that can charge an enemy before the archers can even dismount and prepare to fire a single volley?
Who would guard the 1000-2000 horses while the longbowmen dismount and fire?
Would they just leave them to run around?
In the Game we create all cavalry armies so they can move faster and further on the Campaign map. This corresponds to reality, where all cavalry armies moved faster and farther than armies slowed by the presence of infantry, raiding or seizing important locations. That is the "Strategic" level.
Why would they even risk their horses to enemy fire or even a cavalry charge?
If you even think of the argument that they dismounted before the battle, then why in the name of God wouldn't they just go on foot like the rest of the gang and save about half their income?
Because they were part of the "Strategic" fast moving mounted forces.
Im not saying that they did not fight on foot, surely they dismounted when the situation required them to, however, i believe that it is complete rubbish to remove all chances of them being used as complete mounted archer cavalry since we have many accounts of them being used in such manner.