Mmm... I'm not entirely sure about it having no effect. Depending on what the threshold value is set at, most people won't end up with a tax bill, but that doesn't mean there's no effect.
The few inheritance taxes in place in the US have either $25K or $50K attachment points, so if the value of the assets received is greater than that, then the inheritor has to pay taxes. It might not seem like a lot, but for example, when my grandpa died, even though they were very far from wealthy they had paid off their house, the property had increased in value, and they had around $40,000 remaining in 401-K, annuity, and bank accounts total. And that's not including the value of the other items in the house - tools, furniture, jewelry, etc. The overall value was probably in the ballpark of $500,000, split among three children. Split evenly, they each got around $170,000 in *value*. At a 10% tax rate, they would have each had to pay $17,000 in taxes on those assets, even though the actual money received was only around $13,000. They would have been out $4,000 each due taxes. And they would have been taxed a second time when they sold the house.
It would be even worse when my father died. They had inherited my grandmother's house (which was already paid off), and all of its contents. My dad had no real income at the time, working odd jobs for cash to make ends meet, and living in my grandma's house at the time. The house was valued via tax assessor at about $75,000. My dad would have faced a $7,500 tax bill that they couldn't have afforded - forcing them to sell the house in order to pay the tax.
I don't have an objection to taxing inherited income, but I do object to taxing inherited wealth. I have the same issue when people talk about wanting to tax net worth at high levels in order to get higher tax contributions from the very wealthy. There are a lot of situations where taxing net worth can place someone in a position where they're forced to liquidate real assets in order to pay that tax.