A great thread! I must add some of my own...we are actually not as devoid of fountains as we often think. They are just never working. Regarding the ones you identify...
No. 1 The Rutland fountain has been the subject of discussion elsewhere viewtopic.php?f=49&t=7624&p=109755&hilit=Rutland+Fountain#p109755
but it remains one of the best looking of the city's monuments. I agree fully with your comments regarding its waterworks - and actually the well known Pat Liddy also noted this during a walking tour one Culture Night. Perhaps the City Council might listen to him.
No. 2 I couldn't but agree! What a mess this junction is...a forest of poles. Awful looking.
No. 3 Mentioned before also including the very obvious question: why didn't the mechanism just get moved and relocated to a spot where it might work.
No. 4 The Sheehan Monument was recently removed but I think it will be reinstated at a slightly different location (same junction) Judging from the plans for the Marlborough Street bridge. It was heading for a knock by a bus as it was.
No. 5 That poor feature on Parnell Square - what a disgrace!