Yeah they dont have access to the Long bow, but they gain more than they would on foot, a long bow archer being pushed by two footies is a dead man shooting, if he has a horse and a shortbow, he can easily now put those two footies down and chase, not worry about stam too much and keep his distance with a higher vantage point over cover and obstacles which is huge for archers.
on your last point i'm sorry but it shows you dont use a mount and if you do, it's not well now with the current changes, you can start a fight and never cast a spell as you get focused down and die, there's not balance in that, it's just irresponsible development and balance catering to melee and foot fighters that have been crying grown men for over 10 years there's not a mobility factor for having to cast a long time in a straight line, there's not ability to chase, and if you're trying to escape, you're an easy target to line up on MA or MC. it's not even much of a contest against the other mounted because one hits you for TRIPPLE DIGITS, that's right 100+ per hit. no way to out heal that with interruption or try to out DPS with damage and long cast times with almost guaranteed interruption and moving in a predictable trajectory. and if you're not an Alvarin build then you fall into the Nerf on dex they did to Oghmir months ago and have terrible handling even if you do put all your points into dex
The same thing applies to mages, but you don't have to give up your highest damaging weapons to gain those benefits so you get the 30% concentration and long cast times. A mounted mage can put down and indefinite number of footies faster than any MA
And there is no way that you are getting hit by an MA for over a hundred even if your horse is naked and its a headshot, that kind of damage is only from a longbow which you cant use on a horse. So youll need to provide proof of that claim because if that is true that is an unintended bug. MC isn't even part of the conversation because given equal skill and horses the MC will never catch you in any circumstance and even if both players are equal in skill it is heavily in you favor so if anyone is weak and under tuned its MC.
Without your imaginary 100 damage MA's, a more realistic number is 60 damage full charged arrows to the body on molarium even less with steel but bone armor is much more common. Which with a fat mage you're healing your horse for 40's to the mind with lessers which you can most certainly out heal and that's discounting the fact that MAs do miss shots and you will never miss a Mind heal. So inbetween all your lessers you throw out a fulm on a horse that hits for 90-130 (on an ogh fat mage) and the MA can not heal all that damage back nearly as fast which immediately puts them on the defense.