the fact you get into europa off the back of winning the FA cup tells you what order the trophies are in, in terms of prestige.
No it doesn't ... it tells you the premier league aren't going to be gifted another CL spot by the powers that be, and don't want to take away a spot from the league when the reality is that teams already in the CL usually win the FA cup anyway because teams like Liverpool and City are in the running for it.
Mate, they made CL a prize of the EL BECAUSE it lacked prestige and UEFA wanted to incentivise the competition more. This is like saying because conference league gives Europa it is bigger than the league cup, despite the fact the conference league is fucking pointless and so shit West Ham can be "european champions".