Should a Warrior starts pumping DEX for the new equips?

It's more complex than this.
If you have 3 equips that add 3 dex for example and their requirement is say, 90 dex and you actually have 84 dex. Equipping a earring that gives you 10 dex, equipping those 3 equips and then taking off the earring will not make them unequip.

It's simply that an equipment can't help equip ITSELF but in this case the 3 equips help each other.

Well then the issue then is getting the 170 DEX in the first place to even start equipping items. You'd have to have one hell of a surplus of DEX equips to reach that goal. Egged HTP, DEX shoes, DEX Gloves, CZHelm, etc. It may be more funding than it's worth.