For nearly everything that 'happens' in the sim, a GA is the answer.
Yep, traditionally, you go missed, enter the hold and do long checklists for training. Some outfits have 'integrated' checklists where you use the same list for the systems issue and the the possibly abnormal landing, others have you skip around the QRH hoping you don't misread a title. Is it center hydraulics out or remaining? Is it landing gear disagree or abnormal gear indication? The geniuses at the training building seem to take delight in how easy it is to screw up the page flipping. Perhaps this was an issue in the recent AA overrun in ORD.
Of course, it seems logical to go just ahead and land with a systems problem if you are on final, the plane is configured and you can easily make it. However, if you blow a tire since antiskid wasn't available, you'll get hung for not staying in the air and running several minutes of checklists. Also, if you were a little fast passing 1000 feet (500 feet at some carriers), you'll be in trouble since it's on the tape and you didn't go around. So, you're right, we are spring loaded by training to go around, even on pretty short final when something unusual happens.
In the real world, many times the safest course of action would be to land and sort things out on the ground. I sure won't fault Greesecap JR for his decision to go around or the forced decision to land.