Corrigendum to correct formatting/aesthetic errors previously brought up during proofing process

How cut and dry is the rule of not being able to correct articles once they are published?

While nearly all journals are inclined not to make any changes to the content after publication, they do encourage the use of corrigendum or errata (see AMS policy). However, some publishers allow minor changes to formatting with the version of the old publication archived. This can be acceptable as long as the change does not affect the result or conclusion in any way. In your case its just minor formatting changes and it seems fine in this case.

There are some bureaucratic publishers (such as the one you've encountered) who disallow this feature. This would be especially in the case where print versions are involved to preserve the integrity of the article. Or, just to save the time and effort involved in the process. Hence, it is up to the author to make sure that formatting errors are minimized before making the final camera-ready copy of the manuscript before publication.

Is it worth publishing a corrigendum?

In your case, no. Corrigendum is useful for minor content changes, error and grammatical corrections but I haven't yet come across one for defining formatting errors in tables and uniformity in capitalization.

The publisher is being dishonest when they tell you that nothing can be done now that the paper has appeared online.

The problem is that they failed to make the changes you asked for. This means that the fault is on their end, not yours. They should be responsible for correcting the paper according to your recommendations, and, if necessary, issue a publisher's note indicating that the changes were made as a result of failing to address your corrections.