Actually a good Singed auto attacks quite often, it's not just mindlessly run past you enemy to poison them, you also have to auto attack them while you're doing this for more damage, also when you flip someone you should auto attack them while they are in the air, so yes Singed does some AD but it should never be focused, AD Singed is very stupid.
Also to clear this up his passive hardly gives any hp, if you got 2k mana his passive will only give about 300-400 hp, 3k mana would be about 350-500, a Warmogs would give you more HP than stacking Archangel Staffs, it's a passive that should never be focused on, if you want HP then buy HP items.
Also his builds, why on earth would you stack RoA? That item falls late game because its passive is basically gone, it's an item you will most likely sell late game depending on the situation, a Muramana on Singed? I does nothing, why would you need 1k mana and a bit of AD for? Archangels Staff is good as it gives plenty of AP and some decent mana and also helps his passive a little bit, basically it's a more advanced item compared to RoA, Boots of Swiftness? A good Singed has 3 Move Speed Quints and does not buy those boots instead buys Merc Treads.