Why is "breaking the mould" positively connoted?

The Oxford English Dictionary attributes the early uses of the phrase to Orlando Furioso, where breaking the mold means basically creating an excellent and beautiful work of nature that is made unique and unrepeatable when the mold is broken.

Natura il fece, e poi roppe la stampa.

(Ariosto, Orlando Furioso, canto 10, stanza 69.)

This is the goodly impe whom nature made, To shew her chiefest workmanship and skill, And after brake the mould against her will.

(Translation with fuller context by Sir John Harington, originally published 1591. )

So it was a form of praise for the person so formed, that nature could form no one else like that person. The connection between beauty and uniqueness persisted for a long time. Again the OED:

1786 J. Burgoyne Heiress i. ii. 11 He cannot mistake her, for when she was form'd nature broke the mould.

So the original idea was that the person created was so exemplary that nature wouldn't want to create another one. The focus was on creation and not the waste of a good mould.

The positive connotations remained in subsequent meanings of the idiom, where the focus has shifted from what was created to the more modern sense of a paradigm shift in politics or another area. For example:

1965 A. J. P. Taylor Eng. Hist. 1914–45 269 Lloyd George needed a new crisis to break the mould of political and economic habit.

Here, the "mould" seems to be the current political and economic habit, and Lloyd George (not nature) breaking the mould means breaking that habit. If you support the purpose of the person doing it, breaking the mould is good. Modern usages abound, like this news headline:

Cricket sensation on a mission to break the mould

The mould seems to be playing professional cricket as a woman, another form of breaking a habit or shifting a paradigm. Like the original usage, breaking the mould is associated with excellence, but now the person brings that about herself.

To expand a bit on TaliesinMerlin’s great answer: the original analogy was to casting a statue by creating a hollow mold and pouring molten metal into it. If the mold is intact, you can make an exact copy by sealing it back up and filling it with bronze again. Breaking the mold means the work of art can never be duplicated.

The British political usage seems to invert the metaphor: a dreary situation keeps repeating over and over again, like identical cast-iron parts mass-produced from the same mold. Breaking the mold stops any more duplicates from being made. That is, someone who breaks the mold (mould in British spelling) solves a recurring problem once and for all.

The third usage, where “breaking the mold” is a synonym for “breaking the restrictions,” would make literal sense if something were trapped inside a mold and needed to break it to escape. It might, at a stretch, mean breaking a mold to reveal the valuable item inside it. My best guess is that the people who use the phrase that way weren’t making any analogy to literal molds at all.

This is going to be a difficult one to justify, you don't want the history of the word but the emotive idiomacy, which may be different for every variation.

I am old enough to remember its uses and connotations prior to those most commonly given.

It is said that it became a British catchphrase in the 80's when popularised in the press meaning to put an end to a political pattern of events.

That was considered a positive result by some and negative by others.

Breaking the mould was done for many positive reasons

1. Betterment: A newer copy of a mould would improve the quality; thus, breaking the old mould was a sign of introducing fresher qualities (positive)

2. Weeding out the malformed: A mould with a flaw could keep producing a poor quality copy. If casting "broke" the mould it was considered a self-improvement (yes a loss, but a positive step)

3. They broke the mould when they made them can emotively mean
   a. Thank your deity there will never be another like that (positive)
   b. Sadly there will never be another as good as them (melancholic but aspirational)

Thus we see links to the malaprop "to break [out of] the mould" where one is shrugging off stagnation - again considered a positive trait, and the one actually implied in most popular usage cases, such as changing attitudes towards gender limitations.