Well they usually do.
ME1- Liara
DAO- Morrigan
ME2- Technically everyone
DA2- Anders
ME3- No one in particular
DA:I- Solas
Its just that none have had the bromance between Geralt and Regis.
Liara- Innocent but creepy in chasing dat Shepard booty
Morrigan- Awesome but her stuff was mostly with everyone else, maybe leaning towards Alistair
ME2 squaddies- Well naturally, amongst each other
Anders- The voices in his head
Solas- No one in particular cause thats the kind of dude Solas is
To get that Geralt and Regis bromance feel from a character, we need to be hanging out with a squaddie in particular more often.
Closest a Bioware team got to Geralt/Regis bromance levels is Shepard/Garrus.
I was more attached to Garrus than Regis for sure. Don't get me wrong, Regis is cool and an improvement over the often revolving door cast of Geralt's friends, but you meet him, what, 5 or 6 times in total? It's not the same feel as a companion that followed you for 3 games and fought beside you all the time.
In Inquisition, for instance, I was more interested in Cole, Cassandra, Blackwall and Solas than any TW3 character, and a big part of that is the companion system. Blood and Wine sorta bridges the gap by having Regis around more often than most and fighting on your side a handful of times, so that's a nice compromise, but doesn't change that I simply prefer having a party to being alone in an RPG.
Well, so long as it's not a Bethesda game where companion AI is just stupid.