Why did the Roman army base on infantry?

[Domen]

Infantry will always dominate cavalry. Even today a band of infantry can get up close to a tank and take it down by throwing a hand grenade in the hatch.

First of all - tanks have machine guns to protect themselves from infantry. Also to throw a hand grenade in the hatch, you need to open it first (and this is impossible from outside).

Secondly - we are talking about Ancient Era, not tanks, so please let's stick to this.

The Roman Infanty of the Late Era were very well adapted.

Yet lost on a number of occasions to enemies relying mostly on cavalry.