This is wrong in so many ways
1) If light horses were so useless why did the English expressly request Rounceys over Destriers "for swift pursuit" in a 1327 call to arms?
2) How can you chase down and capture an enemy noble for ransom if you have no horse and are weighed down by armour?
3) How can you more easily escape capture yourself without a horse?
4) How can you as a knight distinguish yourself from normal infantry and thus display your status?
5) How can you get hired as a mercenary when you cannot provide your own transportation?
6) Why would you throw away the extra pay that having a horse provided?
7) Why did horses and especially lighter unarmoured horses out last heavy armour?
Yes it would be daft not to have an armoured horse if you were conducting a head-on charge at a defensible position where the enemy has ranged weapons. However these situations were rare, knights were not required to pass an intelligence test before winning their spurs and horses (unarmoured or otherwise) were still useful in many, many more situations on and off the battlefield.
Basically for a knight it would be a case of buying as a good a set of everything (horse + armour) as they can afford and then work on getting a 2nd better horse and improving the helmet/chest plate with whatever money they earn and don't spend on everything else. Greaves, gloves, mail, arm plates, thigh plates, horse armour, etc can all be improved over time through looting.
of course there were many who would afford both good armor and armored horse, but also many had only so big budget to afford either mediocre armor and unarmored horse, or good armor and horse, i would personally go for the first option.
i never said you can escape easily without horse. but if your horse gets critically wounded, you better have some 27th century instaheal medpacks to fix your legs here. chances are, that you can escape more easily when you fuck up close quarter infantry combat, than when you fail a cavalry charge. also, there is always a chance your horse dies in battle. how long do you think a knight can afford to repeatedly buy a horse over and over and over?
you can easily distinguish yourself as a knight, because you have: your coat of arms over an armor. high quality equipment [unless you were a tard and bought unarmored war horse instead of nice set of plate armor...], a long arming sword [although they were quite common among veteran troops], a shield with your very own crest... do i need to continue?
How can you get hired as a mercenary when you cannot provide your own transportation?
you march on foot genius, you act as if all mercenaries were cavalrymen. in fact them being a proffesional infantry was much more common.
Why would you throw away the extra pay that having a horse provided?
of course you get paid, but there is not always time to get a horse [if you can afford it that is], because soldiers in middle ages were paid either every day, week, or month DURING the campaign, not before.
Why did horses and especially lighter unarmoured horses out last heavy armour?
because horses were vehicles, and because gunpowder was invented, actually heavy armor outlasted horses, as far as i know, a bullet proof vest with ceramic plates can be classified as heavy armor.
usage of horses also fell rapidly after invention of firearms like bolt-action rifles, machine guns, and grenades.
you seem to fail to understand that it was much cheaper for a knight to fight in battle dismounted because: falling of horse would resume in death [and hell horse wont last long enough without armor], he could in heat of battle [now this is a bit loose theory i know, but some knights actually prefered to be closer in action], and also because he could buy top notch armor, rather that mediocre armor and unarmored horse.