You said you do LIT, fasted as well no?
But as far as your speculation, it is just that.. Would, could, should, but in reality we don't know
At the end of the day, it is a never ending debate..lol We can even open up the "LIT vs HIT" argument. It all comes down to preference..
In that debate some people HATE HIT, and some swear by it.. Who is right? Who knows..
I say do what you feel is best, and what works for YOU. My problem is don't make statements like "xx is worthless" because somewhere out there, there is someone doing xx with good results. Lets try and clarify fact, from opinion.
ps. I am not disagreeing with you by the way, just opening up a lil perspective. I actually do fasted LIT cardio on off days, but if it were ME, post workout, id drink my shake first. But then again if it was ME, i wouldn't be doing cardio on my training days.. see where i am coming from? lol