OK, I'm writing this on the basis you did some reading and understand the distinction between the concepts.
The reason strict liability poses such a problem is that it removes considerations of intent, wilfulness, recklessness, and negligence from an analysis of criminal conduct. It poses immediate sentences for breaking a law. The reason it's confined to summary (non-felony) offences is because levying a fine does not result in a restriction of liberty, which, as you will recall, is guaranteed under the Constitution, but for reasonable limits.
So, we assume, rightly or wrongly, that people carrying non-licenced weapons are carrying them in order to commit crimes. We do not consider that they carry them for the same reasons people with licenced weapons do: self-defence. And, given the conditions and circumstances many of these offenders live in, they are more likely to face a situation where they will require a weapon in self-defence than someone like me would.
By removing considerations of intent, wilfulness, recklessness, and negligence from the equation, we are sentencing people to jail terms not for having wronged anyone, but for having contravened a law. It removes any discretion from a judge or jury to consider the alleged offender's intent, and infringes on their Constitutional rights to a fair trial and representation, and liberty.
These may not concern you, but they do concern me a great deal. It's an authoritarian system and it does not reflect the values on which the legal system is based.