I speak as someone who just got out of my one year of conscription two years ago.
Mandatory military service is a good way to weaken your modern military. Firstly, morale is terrible. Apart from the volunteer professional military people, no one in my company wanted to be there. No one. Everyone saw their military service as something to be endured, something to get over with. Psychological problems were common, including a few suicidal individuals. Discipline was as lax as they could get away with, because running a tighter ship would likely have caused even lower morale.
Secondly, the quality of the soldiers was pretty poor too. You've got guys who just graduated from university, guys who have spent the last four years sitting on their butts playing the latest Blizzard release. These guys can't do two pushups without cramping up, they can't run for more than five minutes without puking. They think firing a gun is like something out of Counterstrike, so not only can't they shoot straight, they're also so startled by how loud actual guns are, some of them actually started hyperventilating.
Thirdly, it doesn't really help with the disconnect between civilians and the military. All you've done is create a disconnect between the "voluntary" forces and the "involuntary" forces. To maintain Taiwan's military strength, the parts of the armed forces most likely to see combat are manned almost entirely by volunteer career troops. This means the majority of combat roles in the navy and air force are volunteers. The parts of the marine corps most likely to see combat are also mostly volunteers, if I'm not mistaken. This means the conscripts are mostly sent to the army, or non-combat roles in the navy and air force.
Now, there is one major difference between the US and Taiwan, I think, which means my experience in Taiwan isn't entirely applicable to a US draft. Taiwan's military focuses almost entirely on defending the island against China. If Taiwan's armed forces see any action, you can bet it's going to be in the Taiwan Strait, or on Taiwanese soil. This means there isn't much in the way of choice when it comes to military action in Taiwan; if China attacks, we fight back. It's that simple.
Contrast that to the US. When was the last time the US military was deployed on American soil, to fight a foreign force? When US troops are deployed, they're almost always sent to fight in other countries. This differs fundamentally from the situation in Taiwan, in that the US has to choose to send their troops abroad. However, implementing a draft won't change much, because the drafted troops will likely have low morale, be of lower quality than volunteer troops, and still won't feel integrated into the "proper" military. Hardly someone you want to send to the deadliest conflict hotspots around the world, right?
If there is a gulf between the military and civilian populations in the US, I think it'd be a good idea to try to bridge it. But I highly doubt a draft is the right way to do it.
