No doubt you are correct about how judges have ruled, but by what logic could the first amendment be "incorporated", but not the second? The second amendment is stated in much more absolute terms than the first: the second amendment says the right of the *people* to keep and bear arms shall not be infringed [there is no suggestion that some levels of government can still infringe that right]; the first amendment restricts the types of laws that *congress* can pass [there is no suggestion that this applies to the states]. If just one of these two amendments protected the rights of the people against state and local governments, it would have to be the second.
Doctrines of "incorporation" are ways to interpret the 14th Amendment's due process clause. The 14th Amendment never explicitly says the Bill of Rights is partly or fully incorporated for the states. Some justices (but never a majority on SCOTUS) have held that belief (most notably Black and Douglas). Even today, we don't have "total incorporation"--for instance, it's not necessary for state prosecutors to convene a grand jury before they indict someone for murder (see the 5th Amendment).
There is no reason to think that the 2nd Amendment would be incorporated; in fact, it's illogical. How would you incorporate an amendment that says the federal government can't interfere with state militias? Would you claim that state governments can't interfere with state militias? Or would you claim that state governments can't interfere with any militias? That sounds like anarchy.
The 14th Amendment was passed as part of the Republican effort at Reconstruction. It's whole point is to tell states "behave yourselves." It's due process clause was deliberately left vague so Southern states couldn't weasel out if it (like they had the 13th). It is a check on state injustice, not a blank check for individual rights unrelated to that which are "principle[s] of justice so rooted in the traditions and conscience of our people as to be ranked fundamental" (as Justice Cardozo put it in his opinion for Palko v. Connecticut (1937)).