But still, while this solves the problem of availability (the shardholders could get their stake slashed if they don't publish their secrets after the failsafe condition is reached, because not publishing something on-chain is publicly observeable), does it help that much with secrecy, i.e. not leaking the secret unintentionally and possibly non-publicly?

I guess you could bet on the shardholders not having an easy way to coordinate collusion with somebody willing to pay for it, maybe by increasing the danger of defection (e.g. by allowing everyone that obtains a secret without the condition being met to claim the shardholder's stake?), but the game theory seems more complicated there.