You don't understand why the PJ didn't pick Brueckner's phone number from the 7,000 odd numbers they received?
All I can say is why on earth would they? Why and how would they know/find out his phone number? Your criticisms are totally unrealistic imo.
As for Leicestershire police, they maybe should have let their local boy scouts examine the holidaymaker's completed questionnaires.
Madeleine's was a Portuguese investigation and a jealously guarded one at that as recorded in Amaral's book.
At a time of strained resources while the PJ were supposed to be looking for a missing child, Amaral relates having a weather eye kept on Madeleine's home force by putting senior officers et al under surveillance!
The clincher to the incompetence is the fact that the Portuguese knew about Brueckner.
The PJ tried to interview Brueckner and they failed to do so.
The PJ failed to follow through on that lead and failed to trace him which I think shows someone somewhere in the chain of command was too busy sniffing Calpol bottles and tracing Murat and McCann pings to be too bothered with local criminals.
Get real about the thousand upon thousand phone calls the PJ had to investigate.
Do you really think for one millisecond they did that.
They did what any sensible investigation would do and chose certain limits for checking and started to work through those pings falling within those chosen parameters.
Years later the Scotland Yard investigation showed they hadn't bothered to check out the pings of a team of burglars active in the resort and in contact at the relevant time.
Years after that SY showed the PJ hadn't bothered to check out Brueckner whose criminality they knew about whose pings actually fell within the time span being investigated by two minutes.
I think that might have been a very important two minutes in a little girl's life.