No, it leaves a huge gap: you can't make change for quarters using dimes, and vice versa. If you eliminate the nickel, you also have to eliminate either the dime or the quarter. Mathematically, once you choose the value of the smallest coin, all the other denominations have to be multiples of that value. Otherwise it's possible to create situations where change can't be given.
Last year I drove from California to Montana as part of a multi-state vacation and once I got there all of the coins I was used to accumulating from buying things dropped like a rock! Why? Because there isn't any sales tax in Montana, the price you see is the price you pay. Did I ever get a shock as I did not know this prior to going there. You can buy something for a dollar for just a dollar, you don't have to worry about adding on 5-8 cents per dollar like you do in other states. It was so nice not being given as much pocket change everywhere you go there and really simplified my transactions.