Interesting. I've been a drummer for 47 years and I've heard it all and this discussion in many ways mirrors the still common, "to read or not to read," opinions and arguments.
My own experience is I've taken every side of the opinions over the years. I finally came to the understanding that perfect timing is as rare as perfect pitch. Years ago I was challenged with this, "Show me you can play with a metronome and choose not to use one. Show me that for whatever reason you're not hiding from putting in the work needed to use one." I found out I was hiding. It wasn't comfortable to always play with a metronome. If I took the time I could probably write a dissertation on this but it really always boiled down to this, the metronome interfered with bad habits I had picked up. Over time as the use of a metronome corrected my bad habits the less I needed to use or rely on a metronome.
The opinion of robotic playing IMO is a misconception of what playing in time means. In time does not mean always being on top of and nailing the beat. The best example of this I know of is John Bonham of Led Zepplin. A very different style of music from classical guitar but the underlying rules and concepts are the same. They don't change. While playing blues music Bonham would slightly lag or follow the beat. That slight lag was consistent though and it is what gave the music the strong trudging and sorrowful feel. When he played strong, hardcore rock like in the song "Rock and Roll," he plays consistently, slightly ahead of the beat. It creates a feel in the music of the melody trying to catch up. Bonham isn't considered one of the best drummers if not the best rock drummer because of his chops although he had those. It's because of how he could affect the feel of a song by how he played in time.
I believe what Bonham did came naturally to him but that's not true for most of us. We have to learn it and that's done with a metronome. Like everything else though you have to learn to walk before you run. Once the comfort with a metronome comes, then ability to play around the beat comes. Yeah, learning to use a metronome may not lend itself to the best listening experience but I have no doubt that listening to any beginner with any instrument isn't a wonderful listening experience. If a skilled musician sounds robotic it's not because of a metronome, it's by choice, or the skill isn't as developed as believed or hoped.
We all know what is said about opinions and this is just mine.