I'm not convinced that immersiveness is the difference. I know there is a difference, but I don't believe that it's anything as simple as 3rd limited is more immersive than 1st person. The Holmes stories are in first person and they're so immersive that people have built societies dedicated to perpetuating the belief that they're real. Doyle's Watson voice is so convincing that it creates a powerful sense of immersiveness. Immersivity is a partnership between the writer and reader to suspend disbelief together, and I don't think third limited is a necessarily better tool for that.

I do think 3rd limited cuts out some particular distractions, but first person also cuts out some particular distractions, different ones.