It's one thing for the assassins to die executing their missions like the Hashishin, another for them to be captured, at which point they become liabilities.

The Ismailis (assassins) would often wait around, explicitly to be captured and tortured. If you are expecting to lose the asset, it isn't a significant liability.

The Hashishin installed sleeper agents years, sometimes decades in advance, and improved documentation in the present day makes this even more difficult to do without getting caught.

This is the more significant concern, especially since most conflicts today are inter-ethnic rather than inter-religious. Convincing a Persian Muslim to join a different sect of Islam and then assassinate another Persian is very different from getting a Palestinian suicide-bomber within range of an Israeli politician.