Note: Some potential spoilers ahead, although they're all just rumors at this point.
This is in response to Re'al Dunbar's article Why Batman Being a Myth in the DC Extended Universe is Perfect which raises some great questions and ideas, but I wanted to be able to post multiple links in it, thus a post versus comment.
Incidentally, none of what follows is breaking news. It stems from some posts made by Umberto Gonzalez of Heroic Hollywood back in May and June.
Batman Under Amanda Waller's (Attempted) Surveillance?
First, here is the source for the rumor/report that the government will be attempting to monitor Batman in Suicide Squad:
An article about this Instagram post by Gonzalez can be viewed here.
I'm not sure if we actually know for sure yet whether Suicide Squad is set before or after [Batman v Superman: Dawn of Justice](tag:711870). But let's assume that in either case the government adopts a wary stance towards Batman at the start of the DCEU in BvS and that this will continue into Suicide Squad, regardless of when that movie takes place in the DCEU's fictional world. That would make perfect sense.
Here is another post by Gonzalez of a rumor about an interaction between Batman and Amanda Waller in Suicide Squad which reportedly reveals that Batman and the government disagree about Waller's plan to assemble the Suicide Squad. This would fit into a larger framework of the government and Batman being at odds about the Caped Crusader's methods. Gotham Police Commissioner Jim Gordon has presumably supported Batman and worked with him covertly. But the federal government is undoubtedly a whole different kettle of fish.
A Shadowy Figure Partly Because of the Government
So I agree with Re'al's excellent speculation that this all works toward making Batman a more shadowy and mysterious figure in the public awareness. I should think it would work to his advantage to be seen as a modern myth or urban legend. It certainly makes Batman a much more compelling figure dramatically to be ambiguous from the public's perspective. Many folks may believe he is just an urban legend, a kind of Bigfoot in the big city. Inevitably some will fill in the blank with a conspiracy theory. And so on.
And this would square up well with the inspiration material of Frank Miller's The Dark Knight Returns in which Batman has been in retirement for about ten years, and younger citizens of Gotham in particular have no memory of him. It seems more than reasonable that Batman would be a controversial figure in the public's mind, as to whether on not he is even real much less what he is all about.
But getting back to Batman's (rumored) antagonistic relationship with the government, in order for Batman to remain cloaked from government surveillance it would be very smart for Batman to be perceived more as an urban legend than real.
And I would add that Batman's relationship with the government will also essentially force him to spy upon the government every bit as much as he watches the criminal enterprises that he battles as a vigilante crime fighter. Bruce Wayne the billionaire industrialist will use his insider position to conduct his own private espionage as Batman. A point of dramatic tension could be: How will he be able to do that and yet avoid detection by the government?
This is perhaps where a casting of Jena Malone as Oracle (Barbara Gordon/Batgirl after being disabled by the Joker) will make great sense. Barbara may at times be that digital "eye in the sky" voice in Batman's ear, akin to Jack Bauer's colleague Chloe O'Brien in the TV show 24, or Tony Stark's "Jarvis."
Secrecy as a Uniting Interest for the Justice League
Also, as we know from Man of Steel, the government is also keenly interested in "where Superman hangs his cape" (which either is at that point, or will soon be, the Fortress of Solitude) using spy drones to try to follow him
So I'm thinking that one of the common purposes of the Justice League that will help unify them will be to keep the government out of their business, since the government truly cannot be trusted. This will undoubtedly apply to Wonder Woman and Aquaman, who wish to keep their own respective home civilizations secret (realistically, at least from the all but the world's various government military and intelligence agencies) and sheltered from the rest of the world. Similarly, I'm sure by the time Barry Allen has achieved time travel, the government will be all over him. And certainly the Green Lantern Corps will want to stay out from under the government's microscope.