Knights Templar are more English than the Lancasters

The English are the tower rushers. Network of Castles/Citadels makes the towers powerful in a way that HREs ability to garrison relics or the Rus’ Wooden Fortresses simply don’t. The Templars’ ability to make their Fortresses in Feudal and for only 600 stone, however, lets them Tower rush pretty well with Fortresses. Hospitallers can heal up after attacking and then retreating into Fortress Range (just like the English King), or Serjeants can protect against rams and engage with melee damage. Desert Citadels isn’t quite as strong as the English Network of Citadels, but still it shows that they have the same theme. So, why aren’t they an English variant? Them being all across Europe would allow for it, even if they were more in France historically.