I definitely see your point, but, as I said, all build need to be adapted to fit the situation. Many of my games go 40+ minutes and occasionally 50+. However, this build would effectively be restricted by a game where you are either dominating or being dominated. Once you get your glacial shroud, it actually isn't too hard to get your AA stacks. Before then it is kind of a gradual thing. AA is a good item whether or not you have full stacks. It has good mana and some Mp5, plus it throws on that extra AP that makes your poison really start rocking. Lich Bane, I threw on there more for its stats than its passive, but Singed only gets the occasional harassment hit anyway, so the CD on his abilities aren't that restrictive. Honestly though, by the time you get there you probably should just as well throw on a Zhonyas Hourglass or something to give you some extra bulk and survivability.
Thanks for the suggestion.

*Edit Just so you know, I did mention the time factor in my build, but you probably didn't actually read it.

This is a build designed for people below level 30, so it will not last long like you expect in your guide, making archangles useless because singed has no low cd spells and ROA already gives you all the mana you need. Same thing with Lich Bane, you don't have any spells to cast really, so you will just about never use it and that could be replaced too.

Like I said, please feel free to comment and vote. Constructive criticism is appreciated.