This question is kind of moot because there already is a DCEU continuity. Aquaman directly references the events of Justice League and has a cheeky WW reference in the end. Shazam is directly referential of previous films such as Man of Steel and has a Superman cameo at the end. Birds of Prey has footage from and both directly and indirectly mentions characters from Suicide Squad. And I believe James Gunn has said that we’ll see how Harley gets from where she was at the end of Birds of Prey to where she is at the start of The Suicide Squad.
Right now the only real question right now is whether the Reeves/Pattison’s The Batman will be connected, and I get the feeling that if it is successful, and the other DC hero movies are successful, WB will do whatever it takes to get Pattison involved in a future Justice League movie.
I think a better question to ask and what I think people really mean when they say they want “continuity like the MCU” is if the DCEU should have an overall big story that each movie builds up to, like The Infinity Saga. To that I think while I certainly wouldn’t mind a big DC event, like said Darkseid invading Earth, or maybe something different like the Crime Syndicate or Starro, I honestly like the fact that each franchise is able to do it’s own thing and offer it’s own unique thing. While the MCU has been enjoyable, they do all kind of feel cookie-cutter and a little bland after a while.