That exoskeleton is so limited that "rush for 'power armor'" play style is probably something for meme builds. Completely different from how Power Armor was in Fallout and Fallout 2 where meta rushing for them was worth it, without forgetting this one is not really power armor, only the exoskeleton part. Maybe a 10 STR unarmed juggernaut with max mercantile always carrying hundreds of batteries would do well with it, for that buff to STR when the exoskeleton is on would make quite a difference to fists damage, resulting at 21 STR at level 26 up to 22 with rathound BBQ, a sizable multiplier which is multiplicative with melee skill, yet with a high price to pay from being very power hungry and having a lot of armor penalty for too little protection.
Now, just to be clear: unarmed juggernaut + exoskeleton is a meme build IMO.
Choosing exoskeleton over other armors that either have much better defenses for similar armor penalty, less STR boost and very little defense but movement bonuses and zero penalty or similar defenses at drastically lower penalty looks like choosing shivs over combat knives.