Consider sklearn.dummy.DummyClassifier(strategy='uniform') which is a classifier that make random guesses (a.k.a bad classifier). We can view DummyClassifier as a benchmark to beat, now let’s see it’s f1-score.
In a binary classification problem, with balanced dataset: 6198 total sample, 3099 samples labelled as 0 and 3099 samples labelled as 1, f1-score is 0.5 for both classes, and weighted average is 0.5:

Second example, using DummyClassifier(strategy='constant'), i.e. guessing the same label every time, guessing label 1 every time in this case, average of f1-scores is 0.33, while f1 for label 0 is 0.00:

I consider these to be bad f1-scores, given the balanced dataset.
PS. summary generated using sklearn.metrics.classification_report