Cait is and has always been my favorite Fallout 4 companion, and I have not yet run a single play through of the game where I have not taken the time to stop by the Combat Zone and recruit her. On my birthday a couple years ago my second oldest asked me what I wanted, and I requested a drawing of Cait which is hanging on my wall, framed, right above my desk and beneath my diploma.
So why Cait? It would be easy enough to say that it's because I like redheads and Irish accents. Her personality is extremely grating for some people, but I find her wit and sarcasm to be highly entertaining, even when turned directly against the Sole Survivor's decisions. She may seem callous when she dislikes certain decisions made by the player that are less about greed and more about selfless helping others, but as explained by Oxhorn in his video this is due in a large part by her background, and as a direct result I have no issue with looking past that.
My favorite thing about Cait is that she belongs to no faction, and does not like it when the Sole Survivor aligns with any of the factions in the game. Cait's only allegiance is to the Sole Survivor, and to me that makes her the most ideal companion. That, and also watching her go to town against opponents two to three times her size with nothing more than a modified staggering baseball bat is one amazing spectacle to behold.
Probably the biggest regret I have looking ahead to the impending release of Fallout 76 is the knowledge that there will not be any companions available. Even if there were, they would be hard pressed to be of Cait's caliber.