Whip is a nifty idea, but if you remain at 10' to take advantage of reach you can't also get any martial arts attacks in, which means no bonus attacks and no AC bonus. There are certainly situations where that will be a good thing, but I would think most of the time you're not going to be using the reach quality.
You can make your first attack with a whip, and
if it hits and
if the victim fails their save against Stunning Strike, then you know that you can close in for an unarmed strike and you'll still be able to retreat afterwards without triggering an OA. If your whip attack misses or the target succeeds on their save against stun, then you can decide whether or not to risk closing to melee for the extra unarmed strike, or whether you'd rather spend your bonus action on something else, like Patient Defense.
Also, more broadly, with a reach weapon you can sometimes get in a position where enemies would trigger OAs from you, but you would not trigger OAs from them.
This reminds me of another good kensei weapon: The humble quarterstaff, because of its interaction with Polearm Master. The advantages of Polearm Master for monks in general are well-documented, but the main one here is the extra OA when enemies enter your reach, which gives another opportunity to lay on the +3 goodness from Sharpen the Blade.
Insane Option: By a strict reading of Polearm Master, you can hold a quarterstaff in one hand, and a whip in your other, and get OAs against people entering within 10 feet of you using your whip. This is expensive for ordinary monks (who are not proficient in whip) but could be super-sweet for someone who chooses whip as their kensei weapon.
This option is insane because I'm not sure the strict reading of the rules totally makes sense here.