As I understand your question: sending a basic Assassin to kill the players seems unfair, but not being able to send Assassins seems unfair too.
Why do Assassins seem unfair?
Yes, sending an assassin to murder the PCs in their sleep is kind of a jerk move. Because you are using a challenge that your characters can't overcome.
However, this is not limited to Assassins. You could create a lot of "unfair" challenges: a courtier or diplomat could put the characters on the "to kill" list of every single Clan. Or just have enough Status to order the characters to kill themselves. A hacker in Shadowrun could put the PCs on the FBI's "Most Wanted" list. Or just find someone suffering from leprosy, and send him rub his face on their clothes. Conversely, a bunch of fighters would also be an unfair challenge for a group of courtiers.
By specifically targeting an aspect where the characters can't defend themselves, you are essentially making an impossible challenge. You can, yes. Why don't you do it? Because then it wouldn't be an interesting Challenge.
An interesting Challenge can be overcome.
Think about it. Why isn't any daimyo sending their whole army after the PCs? Why are the PCs always facing in battle things that are roughly as strong as them? Since you are the GM, why don't you just send a dozen half-demon half-dragon half-elemental Tarrasques? Or simply declare "Well, brain aneurysm. Bam." ?
Because that would be boring.
One of the GM roles is to create interesting challenges for the players. And one of the first rules to design interesting challenges is not to make them impossible, but not to make them too easy either. You mentioned Assassin PCs, but surely you don't let them assassinate anyone that easily? Surely there are walls to pass, guards to avoid, insomniac wife to neutralize? Surely if you allowed an Assassin PC to automatically assassinate people without having to do anything, they would complain that it was boring?
Assassins can be an interesting challenge.
Therefore, the GM has to design challenges that can be overcome. But assassins seem like they can't be overcome, right?
Yup. So your role as a GM is to twist the situation so that the players can overcome it. Maybe they have guards, or an insomniac wife, whose murder will make some noise? Maybe the assassin will murder the wrong person? Maybe someone will warn them that the assassin is coming?
The PCs are not living in a vacuum. If they do something that give a motive to someone who has an available assassin, they should be able to realize it (why do you think Shadowrun characters like being anonymous?).
Alternatively, you can just balance your Assassins the same way you balance fighting encounters. But instead of having opponents with roughly the same fighting abilities as the PCs, send assassins with hiding skills roughly on the same level as your characters detecting skills.