Tallow does contain higher amounts of oleic acid than most other fats, and that does have excellent skin moisturizing properties.I agree. These reformulations, as Phil pointed out in another thread I think, also change a number of other ingredients. There’s nothing magic about tallow by itself as a fat. I cannot tell tallow D.R. Harris hard soaps from the non-tallow D.R Harris hard soaps...
Granted, using castor oil and shea butter can also add oleic acid to a soap. It takes some very careful tuning to make a vegan soap that is almost like a tallow soap, and very few soaps will ever get that same (as someone described it) 'unctuous' lather a tallow soap can create. Though to be fair, not even all tallow based soaps are capable of that either.