I have nothing against enclosing "generally" between commas
Me neither. But a comma before it is unnecessary and a comma after it is necessary.
purely because it is, after all, extra information.
Not really. When you preface a sentence with a sentence adverb, it isn't really 'extra information'.
Generally, the more you travel, the more you begin to question your place in the world.
The word
Generally here modifies the whole of the following comment. A comma is necessary after this kind of sentence adverb.
But the OP's question concerns whether there should be a comma
before the word
generally. I say there doesn't need to be. (That's not say that you can't put one there if you mean to tell the reader to make a pause.) If you remove the adverbial
generally you can see the comma is unnecessary:
I believe that the more you travel, the more you begin to question your place in the world.
There's no need to use a comma after a linking
that unless the writer deliberately aims to get the reader to make a pause in her speech. In this case, the sentence adverb
generally belongs in the second clause, so it doesn't need to be preceded by a comma. The linker
that is enough to introduce the new clause.