OK, fair enough, reiner.

He still ends up with only a tulip or lily.

It is a fairly common phenomenon for gay men to both attract and enjoy the admiration of crowds of women.

I think we can settle for the term "ambiguous".

I like your term "having a laugh".  There is something cheeky about the music there, in contrast to his high-minded act in front of his public.  He could still actually enjoy, and has deliberately chosen, his particular form of affectation.

Oh, I certainly agree There's something rather "Christopher Robin" about it - "now, how to amuse them today?" He's enjoying twisting them around his fingers, on his own whim.  I am not sure that ending up with a tulip or lily particularly infuriates Bunthorne - in his own terms it's a victory, because he hasn't surrendered on his principles,  and ended-up as a "foot-in-the-grave young man", as his rival has.

The pictures appeared all right on two computers I tried it on, but I've tried another source for the first one, DB, which isn't quite as good as the first.

I agree about the music being cheeky in parts. I was trying to find a quotation from George Bernard Shaw, in which he thought the music of Patience was very churchy. But I usually find his views on music eccentric. He thought that Utopia Ltd was their best effort - both plot and music.

ELLA
The love of maidens is, to him, as interesting as the taxes!

SAPHIR
Would that it were! He pays his taxes.

ANGELA
And cherishes the receipts!

SAPHIR
Happy receipts!
(All sigh heavily)

If it is churchy, as an antidote, when Bunthorne ends his recitative with "Born of a morbid love of admiration", the last two notes are A-D sharp, a diabolus in musica.

I think its time just to remember the Case Against, as it were.

We have mentioned the misogyny.

Rather more serious is the nature of Gilbert's satire.  There are plenty of examples of genuine social satire (notably in Utopia Ltd) and reiner will probably come up with more examples.

But what is frequently the case is that the satire leaves the object of the satire in place, and indeed confirms it.  For example, the ringing patriotism of He is an Englishman in Pinafore and When  Britain really ruled the waves in Iolanthe.  This was at the height of the British Empire, a generation or two after the brutal suppression of the Indian Uprising of 1857 (I am reading William Dalrymple's The Last Mughal) and just before the Boer War.  Colonial jingoism was to cause a lot of misery, but here it is just a joke.

Again, in Iolanthe the House of Lords are shown as arrogant and pompous, but I can well imagine Iolanthe being quoted by a supporter of hereditary legislation.  It shows we have a Sense of Humour, doesn't it, so we can keep things as they are.

The overall effect can be Smug.  It is the attitude non-English must find infuriating.  We have a sense of humour, so we can maintain thing as they are.

In fact Gilbert had, I suspect, a deep pessimism and even bitterness, so deep he can only bring himself to point out as many paradoxes as possible .  The sweetness and facility of Sullivan's music and its suitability for those with no great musical talent, only cover up the pessimism, and make the smugness all the worst.

In fact there is far more to the works than that, but it is worth considering why they can be infuriating.

Just to say I'm really enjoying reading this thread even if I don't have anything to contribute to the current discussion. 

I have a soft spot for Patience as this was my first G&S - as a lovesick maiden. I particularly liked Grosvenor's song:

A magnet hung in a hardware shop,
And all around was a loving crop
Of scissors and needles, nails and knives,
Offering love for all their lives;
But for iron the magnet felt no whim,
Though he charmed iron, it charmed not him;
From needles and nails and knives he'd turn,
For he'd set his love on a Silver Churn!

Maidens.

A Silver Churn?

Grosvenor.

A Silver Churn!

His most aesthetic,
Very magnetic
Fancy took this turn —
"If I can wheedle
A knife or a needle,
Why not a Silver Churn?"

and so on.

Tragically, the student who played our Grosvenor was killed a few months afterwards on a road accident. Perhaps this is partly why I remember this song with such affection. It's sad that of the four productions I was in, no-one recorded this one.

Oh I can't resist posting the 2nd verse too - the puns are dreadful!

And Iron and Steel expressed surprise,
The needles opened their well-drilled eyes,
The penknives felt "shut up", no doubt,
The scissors declared themselves "cut out",
The kettles they boiled with rage, 'tis said,
While ev'ry nail went off its head,
And hither and thither began to roam,
Till a hammer came up and drove them home.

Maidens.

It drove them home?

Grosvenor.

It drove them home!

His most aesthetic,
Very magnetic
Fancy took this turn —
"If I can wheedle
A knife or a needle,
Why not a Silver Churn?"

Maidens.

While this magnetic,
Peripatetic
Lover he lived to learn,
By no endeavour
Can magnet ever
Attract a Silver Churn!