Well... cameras without mirror boxes are smaller and often substantially quieter and therefore more suited to low-profile photography. Those are probably the biggest reasons why RFs and TLRs have been favoured for street and concert etc. Not because of mirror slap itself.
Anyway, whether mirror slap matters or not depends on many factors. There is no clear answer yes or no. If you go looking for indications that it matters then you will find them. If you start with the assumption that street shooters are all a bunch of irrational leicaphiles or rolleiphiles then you will probably come to a different conclusion! As an SLR and RF user I'd say it depends. Plenty of things I can do with one kind of camera but not the other.
As with many, many things in photography, it is up to the individual to determine the optimal gear for their work.... through testing and experiment.