At the time of the show Banner could easily hide in plain sight anywhere, but nowadays Banner would have more trouble hiding which would lead to more conflict and problems for him. In modern day there would probably be online communities fans of the Hulk with all kind of theories as to its origin. If Jack McGee had thrown the name of Banner, people around the world would have shared pictures of him and he wouldn't have been able to hide that easily.
The show's premise wouldn't work in the world of the INTERNET...PERIOD. The one key flaw in the show that has kind of always irked me (because it WAS my favorite show growing up), is if Banner is a world-renowned scientist, you'd think he'd be recognized WIDELY around the US, if not the world...and not JUST by Jack McGee, who is the ONLY one David seems to fear running into...not the FBI or any other law enforcement, let alone the military after the episode, "Prometheus".
Was odd that Banner never wore a hat while hitchhiking in case McGee spotted him.
Everyone thinking he's dead wouldn't last long nowadays, would be a five episode thing. It's too much of a stretch of plausibility to have nobody do everything about The Hulk but a reporter, in the comics and other Hulk media everyone knows Banner is The Hulk which diminishes all that and opens the door to more interesting possibilities.
Whenever he's not the hulk, to stay incognito when on the run, he could always put on a pair of glasses and part his hair to the other side than David Banner was known to.
Like most shows of the time they set up a premise that never changes along the way, no lasting consequences, it stays the same for the entire run of the show.
Problem with everyone thinking he's dead and going round in cycles around the country with that knowledge what if he bumped into somebody from a previous episode or from his former work life from the pilot? The whole thing would be blown to bits.