Could you elaborate what issues does it come with? I'm biased since I grew up in an area with street names and a consecutive system, but genuinely interested in hearing more.
It's a hassle to have your address changed with every service that wants to send you mail (landlord, utilities, government offices, online shops, magazine subscriptions, etc.), so the change must be considered more valuable than this cost.
In the best case scenario they are very safe choices, that are then reused basically everywhere, sometimes in several places in the same town.
I have seen countless of french towns with "Général de Gaulle" named variations of streets, places, rotaries, small passages etc. It's so overused that it doesn't make sense anymore, people mess with the categories very often (was it a street or a boulevard ? who cares ?)
In the worst case scenario, street names are chosen according to the heroes of the times, or some other political figure that is/will be highly controversial once it has its name on a plaque.
It then becomes an endless battle to find a compromise, avoid further cultural frictions while choosing names that make sense for the town.
For instance in former colonies, street names have often been set to colonial personalities. Some of the (wealthy) residents still support the naming, while others (sometimes minorities) will object to the cultural signification of having these names around for public areas.
These issues are just symptoms of deeper problems, but not using names in the first place just makes things easier.