Archer vs. Kensai
I compared Archer with Kensai and I noticed that Archer is a little more powerful than Kensai.
As you mentioned that Paladin would be allowed to start casting spells earlier, Rangers should become like that. Then, Archer seems very overpowered imo. Even if Archer has additional disadvantage that can not cast spells, Archer is still better than Kensai or at least same as Kensai, isn't he?
Man I was doing the very same comparison a bunch of days ago!
Anyway, I got to almost the same conclusion.
To complete your analysis I may add:
* the Archer need more experience to level up. It's not a huge thing, but being a couple of levels behind does mean something, especially at mid-levels. I'd say this might "off-set" Archer's Stealth ability, Racial Enemy, and an eventual Tracking ability.
* Being restricted to a single weapon type (bows) is much more limiting than being unable to use missiles but still allowed to use ANY type of melee weapon, but while a Kensai cannot even wield any ranged weapon, the Archer can use any melee weapon, though with very little proficiency.
* Kensai's melee AC doesn't fully compensate the inability to wear light armors. They may end up with a similar AC (though a Kensai may actually have better melee AC if he has a good pair of Bracers of Armor, and in my current build they are also getting Defensive Stance to further boost it), but the Archer will be much more protected against missiles, and IR's armors come with nasty special abilities too. Adding to that, the Archer doesn't have to "waste" his arm slot for a pair of Bracers of Armor (aka he can wear baracers or gauntlets to boost other stats/abilities), and can wear helmets too!
Short story: yes, the Archer kit should probably give up his "spellbook", especially considering spells and medium/heavy armor are almost the only thing a True Ranger currently have over this kit (They also get spec ++, but they don't get grandmestery in anything), while the Archer get a permanent/passive +5 to hit/dmg and a good x/day ability.
Compared to vanilla the Archer kit could look nerfed in the described scenario (it's almost as before but with no spells) but KR's Called Shot should be a much more useful/effective ability (counting as multiple abilities), and hopefully I'll manage to improve the Racial Enemy aspect too.Beast Master
And, since you are considering adding animal summoning spells at each level in SRv4, Beastmaster's 'Animal Horde' ability may be very similar to the spells. I think it would be better to change the other abilities such as battle cry which encourages animals.
Well, for this kit I actually thought to focus more on the Animal Companion part (his pet should be a truly viable ally in combat, and if possible I'd like to add some sort of "sinergy" between the two), rather than animal summons. That being said, your idea has some merit, and I also considered the possibility of removing standard spells here too, in exchange for dedicated innate abilities to summon and boost animals.
Btw, I never understood which is more correct between "Beast Master" and "Beastmaster". Mmm...