Prevent password reusing across different sites

Type your password, be sure to include word "honey" in it. Is it reasonable?

No, it's not.

• Random password generators might not support the addition of a specific word.
• It's harder to remember for users who don't use password managers.
• It encourages users to choose a shorter password than they could have used without the condition, just because they want to remember it easily.

If you have a public registration page, then you should assume that any password restrictions you require your users to follow will be known by an attacker. This is because anyone can begin the registration process to see what the password restrictions are. Simply by visiting the page many times an attacker could build their own dictionary of required words and effectively wipe away any possible advantages of having it in the first place.

Now consider that there are some disadvantages, (already mentioned in other answers), the net result of this idea is: Not Recommended.