LTD is a bit funny, because the way you pay the premium (and who pays) alters whether you owe taxes on them or not.
If the employer pays the premiums, and you don't, then you are taxed on the LTD dispersal when dispersed, at your normal tax rate (or whatever is appropriate for the particular time). So if you take them as a benefit (so you pay no tax related to the premiums), you owe normal taxes, probably 15-20% of the total.
However, if you pay the premiums and not the employer, and thus pay taxes on the premium, it's like insurance you take on yourself, which is not taxable - you get the entirety tax-free.
There is a third option, which is what I've always had (usually as my only option, though my most recent employer offered a choice). Your employer can pay them "for" you, but you pay taxes on the premiums. Then it's like you're paying them yourself, you're just getting a tiny raise and agreeing to pay LTD with it. That makes your LTD benefit tax-free if you ever have to use it. You'll see it as a special line on your W-2.
I think you'll find option 3 is by far the most common option out there; it's the only one I've ever seen as a default (though like I said I do have the option if I want to of not paying taxes and making it option 1). But employers are certainly free to not pay that extra fringe benefit, as it is a benefit (though I suspect they can't make it mandatory).
That's part of why 60% is a common percentage, by the way. If you think about it, for many people their total income after taxes is around 60-70% of their total salary. So having 60% tax-free is basically like having the normal salary after taxes.