Here are my thoughts. Avoid Olympic lifting shoes if your goal is to either transfer the benefits from the squat to an athletic endeavor outside of the gym and/or you want to improve the attributes of the body as opposed to just lifting as much weight as possible.
Olympic lifting shoes are shoes with a stiff and elevated heel. The stiffness and height may vary, but they’re designed to allow you, the lifter, to squat deeper by compensating for any loss of dorsiflexion while simultaneously allowing you to drop on the heels. If you’re goal is to lift heavy or to be a better lifter in those shoes, by all means, wear them!
The “problem” or “problems” with Oly lifters can be broken down into two classes.
First, your ankle only works through a limited range of dorsiflexion. If you observe any athlete running or cutting, for example, their ankles undergo extreme dorsiflexion. Couple this with the weight of the athlete and the speed at which they’re performing, training in a limited range is a recipe for disaster. While you may be strong, your ankles may not be strong as you think when asked to go into that range of movement.
Related to the above point, training in Olympic lifting shoes may be masking an underlying imbalance. Now, such imbalance may not be relevant to you, nor may it affect your life whatsoever. With that being said, not recognizing a tight ankle could be making to blind to excessive scar tissue on the Achilles tendon. Worse yet, the tight ankle may be a result of something happening up higher in the chain, such as hamstring weakness, nerve dysfunction/compression or right-left asymmetries.
The choice is ultimately up to you. But in my humble opinion, squatting without Olympic lifting shoes is a true measure of your body’s capability to squat. And furthermore, the transfer to explosive athletic activities is much better without them.