As long as someone else has nukes, no one would want to deploy AShBMs on SSBNs, since:
A) the other side won't know what warhead your missiles are carrying until impact, and there is a chance they won't wait to find out for sure before launching their nukes in reply.
B) by placing tactical weapons on strategic platforms, you are making those strategic platforms a legitimate target for enemies.
Normally, with a limited war, there will almost certainly be red lines drawn in the sand, as it were, by both sides with tacit agreement to not engage certain targets. SSBNs would almost certainly be top of that 'untouchable' list.
But that won't hold true if one side puts tactical weapons on their SSBNs and starts shooting them off in combat.
When the other side start engaging your SSBNs in a systematic way to counter AShBMs, they are also taking out your second strike capability and so now you are wondering if they are planning to escalate to full nuclear war and are laying the groundwork for that. So that means you are faced with the 'use 'em or loose 'em' dilemma.
Suffice to say, putting AShBMs on SSBNs, much like the proposed U.S. Prompt Global strike missiles, are as big a liability as they are an asset, and in all likelihood will be effectively unuseable against another nuclear power because of the unacceptable risks it will inadvertently kick off an all out nuclear exchange.
Such weapons can only be used to bully non-nuclear states, but that has never been high on China's military modernisation priority list.
Better than I thought! 
