In defense of Wednesday having a few emotions:
Any of the older series or the films always depict her as cold and emotionless because that's the joke. She's the only one in her family that ever has that trait, but it's never explained as any kind of supernatural compulsion or anything. The Wednesday series has decided, of which I am thankful for, to depict Wednesday's cold and calculated demeanor as an emotional defense that she has been using for years up to this point. This is obviously because the new series is more than just a comedy and Wednesday is now the lead instead of just a a one-note joke that shows up occasionally (sadly that's what they made Fester in the new series). Her demeanor even makes her an outcast amongst her own kind, as others are perfectly capable of showing emotion. But Wednesday is human and I think the series wants to explore her humanity a bit. There should be points where a little happiness/sadness/excitement squeaks through. Maybe even a little fear too. What's great about Wednesday is when this does happen you know it's a big deal.
This actually isn't the first time that Wednesday has shown some emotion.
In the Broadway musical she begins to come to terms with how being in love starts to make her think a little differently. One of her songs about it is my favorite in the show.
I binge-watched Wednesday over the last couple of days, and I really enjoyed it. I'm not as bent about taking her 'off brand' as some people seem to be. But then again, my memories of the character are from the black-and-white tv show from the 60's, and not anything that came later. In that series, Wednesday is a lot less one-note: She plays with dolls, she cares what other people think, she is helpful, she likes to dance. She's not this emotionless outcast, just a little weird and macabre like the rest of her family.
Something to consider: in the TV show, she was like 6 years old, and in the later movies, she was more like 13. In the Netflix series, she's 16. To expect a person to retain the exact same personality during 10 of their most formative years is just silly. I felt the new series portrayed her just fine, and I enjoyed the character growth.
I think when people look back on a show, their feelings about characters get filtered through a simplifying lens that pares the characters down into the bare essense of their interpretation of the character. Back when Terminator 2 first came out, my girlfriend at the time said she hated it, because the T-1000 ran when giving chase. Her argument was what made Arnold as the Terminator such a scary adversary was that he never ran but was relentless and never stopped coming--despite the fact that there are scenes in the first move where he does, in fact, run when giving chase.