(We were working on "foundation models" too, so it's not just being out-of-dictionary in the final model that's a problem but being out-of-dictionary in the foundation model which is more expensive to train.)
We were doing OK with character based models for classification but people believed that storing the "dictionary" inside the neural net was not a good use of the neural net so there was a lot of enthusiasm for tokens.
Meanwhile I felt so sure that schemes like Word2Vec were doomed that I had left an earlier project using RNNs where the goal was text understanding with a foundation model made by training an RNN to write fake abstracts for case reports from PubMed.
When byte-pair encoding was introduced I remember telling people in a meeting that it was the first tokenization scheme we'd looked at that I could endorse.
I have to admit though that I wish we could work at the character label.