Of course they feel cheap. The amount of nickel in a quarter is worth way more than a quarter, and the pennies, copper is something like 50x the price of a penny.

At this point they should be stamping coins from stainless steel that is alloyed to give it tints for different denominations. It would be much more durable and far easier to handle.

The problem is stainless steel is a super-material. Its the greatest form of metal every created by humanity. Its very, very HARD, and it near perfectly strikes the balance between hardness and elasticity (with that balance moderated by the level of carbon in the alloy for hardness vs elasticity) that is so valuable about tool materials. Its why stainless steel is the go-to material for premium knives and tools.

Its actually the hardest, strongest form of steel currently known. And so would be actually just as hard if not harder than the steel presses used to mint the coins, and harder materials like carbide would shatter under the pressures. And to make it all worse, stainless steel cannot be heated to press it in the presence of air, which will chemically react with it and ruin it, causing forging operations to crack the steel grains, destroying the material.