I don't think you understand how big SW is.
First, there are about 100 Quadrillion beings (10^17) in the SW galaxy.
With Euro crime rates, the SW galaxy would have:
Petty Crime: 5Γ10^15 per year (5Q)
Serious Crime: 5Γ10^14 per year (500T)
Murder: 10^12 per year (1T)
Litvinenko style murders: 10^10 per year (10B)
There's just too much crime for everything to be transmitted. As long as your name isn't "Skywalker" or "Solo", and you don't do "high" enough crimes like kidnapping a Moff, you can slip through the cracks.
Second, with a fast enough ship, you can outrace the APB sent out for you; which you can see if you ever watched ANDOR -- specifically S1E11: Daughter of Ferrix, where the lag it takes for a standard Imperial patrol cutter to run a transponder is significant:
"How long on the ID?"
"In the queue, sir."
It took about 1.5 minutes to run that ID, and it was a Alderaanian one, so it would have been higher in the queue than a random no-name world's ID.
In season 1 of Andor the Imperial Security Bureau discovers who Andor is and deems him a fugitive.
In episode 1 of season 2 Andor is just chilling in an Imperial facility and no one cares.