One of the issues is that the 4473 is a "federal" charge but for prosecution at the state level, states would need a concurrent law prohibiting misinformation on the federal form in some sort of way. Currently, it is true that the ATF and other government alphabet agencies largely ignore 4473's except when they are already investigating a subject for other crimes (one straw buyer case that went to the Supreme Court was where they suspected the cop of pulling a bank robbery and were investigating him for that.)
Thus, for widespread elimination of straw buyers, you will need state and local law enforcement and prosecutors along with empowering state laws to get at them. The lowest hanging fruit is felon in possession of a firearm but proving an illegal attempt to acquire a firearm is a far different thing that requires proving intent beyond a reasonable doubt to a jury. Far easier to prosecute is the possession charge where it requires no knowledge from the suspect and simply for the police to demonstrate possession of the firearm by a prohibited person.
There is the same problem charging other 4473 violations such as lying about substance abuse, lying about being a citizen, lying about most other disqualifiers on the form as well, etc. The easiest, if you will, would be the denial of a felony record and that would be no slam dunk. Due to plea bargaining and the vagaries of state laws, a defendant could make the reasonable reply that they were unaware that they were a felon when they answered that form and the prosecution would have to show knowledge necessary of whether a defendant had intent to violate the law by knowing they were prohibited and pursuing the sale anyway.
Another way of dealing with straw buyers would be stings, and that sort of things that resulted in such famous actions as the Fast and Furious.
The other ways to get these straw buyers is a) charging them with running an unlicensed firearms business (but this will catch up collectors and frequent traders as well), or b) allowing them to be charged for the crimes committed with firearms that they sold as a felony accomplice to that crime (which might also get an innocent seller into trouble).
We as a community need to figure out a way to address the straw buyer issue as that constitutes roughly half of the firearms used in illegal activities and that means that new state laws that will crimp some folks desires for unpapered firearm transactions and frequent firearm traders engaged in private trades. It also means making prosecutions of such a priority for state prosecutors and law enforcement. The alternative would be a hypercharged built up ATF with large increases in personnel, new federal laws, additional prosecutors, etc.
Project Exile, done in part with the approval and suggestion of the NRA, demonstrates that vigorous enforcement of firearm laws by federal/state/local taskforces can reduce gun crime in a selected city (Richmond) that is suffering waves of violence. That requires political will that is lacking at various levels of government and is why something like that was not pursued in cities like St. Louis, or Chicago.