While T3 appears to be the most metabolically active, all thyroid hormones (T4, T3, T2, T1, T0) have non-genomic effects many are not aware of. All this means is that they can exert an effect on the cell at the plasma membrane (surface) or cytoplasm level, whereas the primary effects of T3 are at the cell’s nucleus (after conversion from T4). In other words, T4 exerts these non-genomic effects outside of the nucleus, and before its conversion to T3. So to say it is a prohormone (storage hormone) with no effect is a false statement, because it does have an effect in its unconverted state, as T4. 
Hair needs T4, because it lengthens the hair growth phase.  My Free T3 has been below range, mid-range, and over-range, but my hair was still not right at any of those levels. Only since adding T4 to get my Free T4 above mid-range (and lowering my desiccated dose) has both my hair texture and volume improved. It should be noted that hair loss is a symptom of both too much and too little thyroid.
In one experiment on dogs, T4 was administered both topically and orally. In either case, there was an increase in both the rate of hair growth and in the number of hair follicles entering the growth (anagen) phase of the hair cycle. 
T4 converts into other essential metabolites besides T3. These cannot be made from T3. Just like T4 is deiodinated (converted) to T3, T4 can also be deaminated (converted) to tetraiodothyroacetic acid (tetrac). Tetrac has been shown to inhibit tumor growth, while T3 and T4 stimulate it.  If T4 is eliminated, then there is no source from which to make tetrac, which may be just one of several metabolites that can only be created from T4.
T(1)AM (3-iodothyronamine) is another biologically active T4 metabolite which has nongenomic cardiac effects. This metabolite induces opposite effects from those stimulated by T3 and T4, such as decreased heart muscle contractions and decreased heart rate. Both T3 and T4 have multiple nongenomic cardiac effects, and an equilibrium between T3, T4, and T(1)AM levels is essential for heart health. 
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