It's a good question, but I'd like to point out that you can still ride things that are unsuitable as mounts:
Ride Skill
You are skilled at riding mounts, usually a horse, but possibly something more exotic, like a griffon or pegasus. If you attempt to ride a creature that is ill suited as a mount, you take a –5 penalty on your Ride checks.
So even if the eidolon is undersized and lacks the mount evolution, you can still try to ride it at a -5 penalty. All the feat and evolution do are remove that penalty.
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You missed a second penalty that is much more important. It is a Move Action to control your untrained mount instead of the Free Action to control a Trained Mount.Which wouldn't apply to an eidolon.
Why not?
Do not use intelligence for a reason, it doesn't understand how to act as a mount because it is NOT suited to be a mount without the Mount evolution. Do you understand how to act as a combat trained mount? It is far more then just knowing what your rider wants, you have to know how to move properly with someone on your back.
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A creature you summoned and can communicate with is under your control automatically(CRB-354). You can tell your horse-dragon eidolon to attack a particular foe or move a certain direction by shouting from thirty feet away. I don't read the rules as you losing that ability because your sitting on the eidolon. You don't need to worry about the "Control [not combat trained] Mount in Battle" part of the Ride skill (CRB-104).
Maybe your thinking of the "Fight [you get to make an attack on top your mount's] with Combat Trained Mount" part of the Ride skill, which is a free action. As the mount evolution specifically calls out the eidolon as "skilled and formed" as combat trained mount, I'd can see this (your?) point. If you want to make a ride skill check to attack in addition to your mounts attack, you do need the mount evolution. Which in itself is an important second penalty.