I think Thai boxers, Taekwondo fighters, Capoeiristas, and Savate fighters - all of which specialize in kicking - would disagree with the Shaolin kung-fu instructor on this as a general tactic. They have no problem kicking an opponent who is free to move around. Which is why you really have to nail down the underlying principle behind the statement first before assessing its merits and practicality.
You mentioned two details that I'll focus on:
1 - Your opponent's feet are both on the ground.
2 - You are manipulating your opponent by way of the arms and wrists and possibly other methods.
This paints a picture of seizing your opponent's arm, possibly elongating it or pressing down on it. The goal is to get your opponent to become immobile in order to deal with the fact that you're doing something to his arm. That's the underlying principle here.
I picture him being pulled diagonally towards you, putting him into a lunge position, over-extended in one direction. I also picture him in a horse stance, with you performing a standing arm-bar on his shoulder/elbow, bending him forward.
This immobilizes your opponent while making him deal with a decoy attack. The decoy is you seizing and controlling his arm. You actually don't care about his arm, but he doesn't know that. His attention is all on that. The real attack is whatever else you want to do. But given that you're probably using your arms to control your opponent, that leaves your legs as the only weapon you can use. Maybe also a headbutt or a quick transition to an elbow or knee, depending on range.
Range was specifically a concern in the original question. Kicking range is typically long distance while not holding onto your opponent. But think about angles here if you do have control over your opponent. If you're holding onto your opponent by way of his wrist, you can lean back and use a high round kick to his head. You can perform a front or side kick to his torso. You can do a low-angle kick to the inside knee of the leg furthest away from you. You can sweep the leg closest to you. You can knee to his head, if he's in the bent-over position. Plenty of possibilities. The fact that you're close to your opponent and controlling his arm doesn't mean you can't kick him.
The other element of this is your physical connection with your opponent. You've grabbed his wrist or arm. That can communicate any changes in your opponent's movement instantly. This sensitivity is a soft-style skill that takes some time to get good at, but is pretty easy to understand.
You want him immobilized so you can land those kicks accurately. If he's moving around, you'll have to recalculate your attack, which takes time and generally involves a lot of error. Kicks are generally slower than punches and more telegraphed. They're easier to dodge. Which is why you need to pin his feet to the ground. You do that by seizing his arm or shoulder. And the sensitivity you have to his movement, communicated through that connection, will tell you when he's about to move. So you'll have a small window of time to kick and get out.
Most kung-fu styles utilize this strategy to some degree. One style that comes to mind most is Northern Praying Mantis. Other styles include Northern Longfist, White Crane, Hung-Gar, Choy Li Fut, and Mitsung Lohan.
One other thing to note. As a martial concept, it's fine. But don't try to generalize this into thinking you should limit your kicking to only when you've controlled someone's arms and immobilized him. That's not the intent of this. Instead, it's telling you there's a scenario where you can get a small, fleeting advantage if you're fast enough. That's all. Don't broaden its meaning any further than that.
And it's questionable how realistic this is. My advice is try it while sparring. Try to find an MMA or Sanda guy to try it on. See if you can make it work for you. A lot of martial concepts are nice ideas, but just don't work very well when you put them to the test. In this case, speed and control are the main weak points.
Hope that helps.