But it's not, though. That's part of the problem - the right to bear arms is explictly constitutionally protected.
Remember, the history and deveopment of the US and that of the UK are very different. Even when gun ownership in the UK was far less restricted than now (which is not as long ago as you might think), it was never as culturally embedded as it is in the US, at least in part for the type of reasons briefly mentioned above.
So ... while we might like to be in a different cultural place than we are, we are where we are. Wishing otherwise amounts to "well, I wouldn't start from here".
And where we are is that it's constitutionally protected. And that means that the Supreme Court can, and believe me, WILL strike down any laws a particular government come up with if that government tries to tread on constitutionally protected rights.
It is possible to narrow the field, and impose some restrictions .... such as covering criminal records, or residency requirements.
Also, remember, it's a state v federal thing. US states all have their own governments, and they very jealously guard their areas of "competence" from federal interference by the national government.
It is, if you like, similar to the Scottish parliament and Welsh assembly getting very uppity if Westminster tries to dictate to them in devolved areas. Westminster would be told to bleep off, and US state governments tell the federal goverment the same thing. Which is why gun laws vary so much from state to state. In some places, getting a concealed-carry permit is pretty easy, and in others, near impossible if you aren't in law enforcement.