Because UA is betting that people won’t try breaking them apart. Also, becuase it’s really early for purchasing summer travel.

I mean, that’s not really true, but even if it were, wouldn’t you check in again at SIN if a company were going to give you $1500 to do it?

A competent UA agent can check your luggage through to MAA and may even be able to print your SQ boarding pass, although if they can’t, you can pick one up at the transfer desk at SIN. The primary disadvantage of buying separate tickets is that you’re not protected in case of a delay or cancellation — and delays on SFO-SIN are not uncommon. If UA gets you to SIN too late to catch your flight to MAA, SQ is under no obligation to rebook you.