I realise this is all obvious to the thinking people we have here, but just setting it out:
It's one of those things that the proscriptive grammar books claimed is not allowed, the same as split infinitives. Previous generations were educated by rote, the rote being what just one person decided was good or bad and put into a text book – independent thinking (or poetic expression) not permitted.
Just because a word comes after a full stop and has an initial capital, does than make it the start of a sentence? (Give me some rope here.) "And" and "but" are clearly connecting words, attaching the succeeding clause as a modifier to the preceding* clause, so the clauses really ought to be in the same sentence.
In written English, punctuation
can be used to identify the logical structure of the clauses specifically (I avoided a split infinitive there!**), so I submit any "sentence" starting with "and" should actually be a sub-clause of the previous sentence separated by a lesser break than full stop, but the consequence may be very long sentences and paragraphs (as used to be common) when it may be easier to get the point across by breaking it up and even splitting a clause across paragraphs.
If the text is actually a script, then no holds are barred. The punctuation needs to indicate lengths of pause, for effect or to aid the listeners' digestion.
It was not uncommon (a generation or two ago) for written sentences to be overloaded with commas (IMO) where they could be just implied:
<clause 1>, and, <connected clause 2>
That is clearly indicating a dramatic pause rather than logical structure.
* I just spotted another interesting point: why does "succeed" have a double 'e' but "precede" an 'e' on the end?!!!
** By avoiding the split infinitive [edit: incorrectly!], I've thrown the adverb (a verb modifier) to the end of the sentence so the reader ends up having to parse the whole sentence in one go rather than step by step. I don't care what the old-fashioned grammar books say, it aids understanding to have the adverb near the verb! There is a story where an interpreter went silent during a long rant (in German, I think) being unable to produce the English translation because he had to wait for the verb at the end (when English puts it near the beginning).
