There are altenratives, copper/gilding metal expanding bullets for rifles and pistols, and things like bismuth for shotguns (although they seem very expensive).
There is not really practical realistic alternatives.
Shotgun shot is very different because they are projectiles much smaller than the bore, this means they still rearrange and constrict as necessary.
They can even be kept from coming into contact with the bore of more open chokes with the shot cup. The shot does not need to engage the rifling like a bullet does to work.
They also are intended for use are very short range, where the lack of density is not as critical, and from a platform that can have the payload more varied in weight and size than most other firearms.
Did you know that a lot of lead alternative shot also contains a large percentage of lead?
Bismuth is primarily produced as a byproduct of mining lead. A very small amount in comparison to lead is mined, and the supply cannot easily be adjusted upwards to meet greater demand.
In 2007 bismuth prices went up to $14 a pound from a little increased market pressure. That is how volatile and limited a commodity it is.
By comparison lead is generally under $1.
The bullet is one of the most expensive components in ammunition, and is by far the highest amount of material used in a lot of calibers.
Ammo costs could easily be several times higher than they are now if bismuth had to be used and the consequences of demand increased the cost. It is less expensive now than it would become, and it is already expensive.
In addition to generally wanting a material of high density, even many less dense substitutes are not legally allowed:
Federal law prohibits most inexpensive metals from being used as bullets. Technically it is handgun bullets, but the ATF has extended it to many popular rifle calibers, applying the law to many calibers if they are chambered in a firearm technically sold as a handgun.
For example AR and AK pistols mean that .223/5.56 and 76.2x39 ammunition is handgun ammunition as it pertains to the law.
Even the .308/7.62x51 is considered handgun ammo per the ATF.
So you can see that not only are handguns covered, but most popular rifles as well.
The law makes it illegal for common elements like iron and steel to replace lead. Even various types or quantities of brass are illegal.
So you couldn't even have steel bullets like you have steel shot because it is already illegal. Some common metals form oxides much harder than the metal itself, that can damage a barrel. This includes many metals, but a great example is aluminum, where the oxide aka corundum is the hardest element after diamond, and is used for grinding and shaping many things, and even makes up the grit in a lot of sandpaper.
Copper costs a lot more than lead, and would dramatically increase the price of ammo.
There is also other concerns, lead is easy for your average person to work, having a low melting point, and being soft and workable even at room temperature.
The melting point of most materials puts the creation of quantities of bullets outside the realm of the average person.
A person could make individual ones on a lathe, but that would hardly allow for the creation of them in much quantity.
Molten lead at the right temperature also allows a dual purpose of annealing hardened case mouths. That would also be lost.
So most alternatives would increase the cost of ammo significantly or be unsuitable or illegal.
Contrary to various antigun statements increased cost also does not impact criminals, who go through very small quantities of ammo (some criminals even have the same rounds in a gun for years, or mixed types of ammo because they use it so rarely and fire so few shots that they added only the number of expended rounds back to the magazine.)
Nor does it impact individual killers where the cost of ammo is insignificant, nor the type of killers that don't plan to be around to pay for any debt they may incur.
The people primarily impacted are recreational shooters that go through large quantities of ammunition by comparison on a regular basis.