Because they felt the need to be so slavish as to keep the original character's name, this movie could only be in the Cineverse with no connection to its Toobworld counterpart. As far as the Toobworld Dynamic is concerned, there is only one Robert McCall AKA the Equalizer - and that is the late Edward Woodward.
I would have preferred to see them keep the title of "The Equalizer" - after all, it's just a job description - but give Washington a new character to play. Then it could be assumed that he took up the mantle of the job after McCall retired or died. (Woodward passed away in 2009.)
And that connection wouldn't even have to be made if you don't want to alienate any newbies to the concept, who might not be interested in tracking down the original series. But at least it would be out there for the fans of the original series.
It just seems like they're trashing the memories of the show by erasing them.
This is the same problem I have with the upcoming remake of 'The Man From U.N.C.L.E.' I think it would be great to bring back the spy organization, but have the stars Tom Cruise and Armie Hammer play new characters. Without Robert Vaugn and David McCallum in the roles, there's nothing inherently magical about the names Napoleon Solo and Illya Kuryakin. Cruise and Hammer could just as easily win over new fans to the franchise with new names without alienating the previously established fanbase.
Speaking of Tom Cruise, he and the other producers of the "Mission Impossible" movies were heading in the right direction with the first film by creating all new IMF agents. But then they had to bring back Jim Phelps - but without Peter Graves to play the role. And to top it off, they had to trash the memory of that character. I've seen bad remakes of TV shows as movies - 'Sgt. Bilko', 'McHale's Navy', 'The Wild, Wild West' - but that was just incompetency in the production when it came to directing, writing, and casting. This was a deliberate spit in the face of the original and the fans.
Someday I hope somebody buys the rights to "Jerry McGuire" or some other Tom Cruise character and makes him a repulsive figure. Let's see how he likes that!
In other news about 'The Equalizer', Michael Sloane, who created the original series, has inked a deal to now write a novel about the character. So that means Robert McCall will be joining a very select club - as a Multiverse character (Toobworld, the Cineverse, and BookWorld.)