You will just make archer OP if you increase fire rate and accuracy anymore, people will just play archer outisde cavarly making infantry useless.
I think right now archer are in a good spot, i can agree with you that light archer (only them) could have the same speed as infatry so they can still run away but not outrun them
If you play some meta tactics with 3 cav 3 shock infantry, you will see them running around a lot and you can't catch them while your men get killed by cav.
In random games they have no reason to run away, because they don't have ranged weapon like archer do, if you make archer be able to outrune every infatry with just 3 archer you could beat any other infantry combinations as you can run - shoot - run and they will be never catch you
People didn't take archer in tournaments not because they think they are weak or slow, but just because one single cavalry capatin can delete an archer unit in few second expecially with 2 hand weapon like glaive or bastard axe
Until a captain can move alone without risk to kill enemy units archers will be always in a bad spot. Yes, i can kill that rambo cav player coming to me but in the meantime he already kill 5 of my men
Archers are not even close to be at a good spot right now. They are far far away from being there. The AI is way too passive, and engages targets all over the place, behind them from the side or they just stand there looking like they are overwhelmed. They need a very narrow field view and they don't have that now. You said it yourself, no one pick archers in tournament because 1 cav can kill them alone. Because of what I just said. So you are actually agreeing with me without realizing it. With a narrow line of fire, higher fire rate and better accuracy you can get that single cav before he gets you, IF you have skill. 18 archers vs 1 cav, archers should be able to OWN that single cav. Like they did before 1.5.0. If archers don't get picked in tournaments it is because there is something wrong with the archers, and NOT the cav. The cav is in a good place, archers are NOT! I refuse to listen to players that got some idea that inf should protect archers from enemy inf and cav, it's such a stupid tactic. Archers should be able to take care of them self. If cav want to attack those archers, the cav need to use all his troops, what I am trying to tell you is that this will make rambo tactics obsolete.
If inf and 2h want to get the archers, they need the support of cav, and cav has to use full cav attacks. The 2h needs to be in formation with his team behind shields and not run alone with mach 3 and kill the archers in seconds all alone with no casualties.
Movement speed : If archers are getting attacked with that formation of inf and 2h I just explained, even with no cav to support the enemy, then archers will have to hold fire and run. The second archers hold fire they are not making any damage. Then they have 0 fire rate and 0 accuracy. And If the archers want to escape the attack, they will have to hold fire pretty soon and run like hell. There are different ways to deal with this situation for the inf and 2h. Cav can attack archers with full force, and keep them from running, while the rest of the team engages in melee fight. Or cav can attack with full force and the formation of inf and 2h will catch them with ease. You can also split up, 1 group of inf can go for the running archers and keep them running, while the rest deals with the melee fight. The counters to strong archers are vast, if you are not being lazy.
Inf vs archers : If inf is faster than archers, there is no point of being either class. Is boring af to be inf and catch archers with no fight. And being archers, the second inf comes for you it's over, you can run all you want, they will get you with not 1 single unit lost. This is a tactical game, and there is no tactic in that. The maps are not infinite, and lets say archers in melee mode would have same speed as inf, then they would never be able to do what you fear. That they can build distance and start making damage on inc inf. and keep doing it. And even if archers were faster than inf, like back before 1.5.0, inf would still be able to catch them, IF you have skill. Use the terrain, and shieldwall when they stop to make damage.
Archers are the key to unlocking captain mode. We are in this situation today because archers were nerfed to hell. 1.5.0 removed archers from the equation, and rambo tactics and inf metas was born and made this mode so damn boring.