That is exactly the use case for Update although the documentation about it won't give you in depth insights.

Shortly, once evaluated expressions are internally marked as such and won't undergo reevaluation for efficiency purposes. Unless something triggers them, like Update.

validQ[_] = True;    
Update[func];

{foo, func[a]}

{a, a}

In[1]:= func[arg_ /; validQ] := arg
        foo[a_] := func[a]

In[3]:= validQ = False;
        foo[p]
Out[4]= func[p]

In[5]:= validQ = True;
        foo[p]
Out[6]= p

I tried that, changing all to SetDelayed, but also didn't work for me…

Interesting question for which I have no answer unfortunately, but I hope to find out by leaving a message here…