While your point is well taken and I fully agree that Matt Gaetz is a completely disgusting slime ball, AT BEST, there are several problems with this argument.
The first being the Justice Department didn't drop charges against Matt Gaetz because charges were never brought in the first place. You can't drop charges against someone who is not being charged.
The second is that I don't see any reason that federal prosecutors would have a motive to protect Gaetz. Federal prosecutors rarely bring cases that they can't win and if they feel the evidence is lacking, it must be significant enough to warrant pause.
And the third is that the US justice system doesn't work by "mob rule." Pressuring the Justice Department to charge someone isn't how the Justice Department works because it is not a political institution. Charges are brought and should be brought irrespective of public opinion. This just opens the door to political prosecutions.
This is not to say that Gaetz is innocent of anything, but the standards for proof beyond a reasonable doubt are extraordinarily high for a reason. If you change that for one person, we're all in trouble.