That didn't work against Nas, why would it work against Kendrick? Cole tried this to a lesser extent while also trying Jay's "one hot album" thing - which once again did not work against Nas and clearly didn't work against Kendrick.
Ironically the best attack on Kendrick would be similar to Not Like Us: an anthem/banger that straight up clowns him. You're short, you don't have any bars people remember, you dress like shyt, etc. I don't think Drake was capable of making anything as potent as Not Like Us so he was always gonna lose, but he would have done better with a fun yet vicious track instead of Family Matters which was way too serious (and unfocused).