The nice thing about more "classical" approaches -- a simple BoW random forest or MLP, for example -- is that they're typically quick to train and experiment with, and they make for great baselines, if nothing else. So I doubt that we're in danger of people forgetting about them entirely. If people do, they're leaving quick, easy solutions on the table.
I do like your idea about triaging inference between smaller CPU vs. larger GPU models based on whatever signals. I haven't tried that before, but a project my colleagues worked on did some triaging between regex pattern-matching vs. model inference. Basically, the regex pulled some of the data out first if it matched very specific, known patterns, and then the rest was handled probabilistically. I guess the effectiveness of that sort of triaging approach depends on how strong and clear your signals are that let you choose one path over the other.
In some projects I'm working on, I'm seeing close to 95F1 score using deep learning to do token classification based NER. However, using non-deep learning approaches (still training statistical models) I can get to 91F1 on my use case but have a much faster inference and not need to use a GPU.
I'm similarly optimistic about LLM, but fear that a lot of other really useful workhouse algorithms and strategies are going to be pushed aside and people will forget about them.
Back to my use case, some strategies I'm looking at are using cheap and fast CPU powered models/smaller models for inference and then based on certain signals decide whether a particular instance should be passed to a GPU based model for better accuracy.