The whole dying part in the storyline is so out of whack. They just drop this bomb halfway through and expect people will go explore rest of the - now unlocked - city. Like couldn't Victor just pull-out burned chip, say all is dandy and then V would get Johnny's hallucinations, only for 'Meet Hanako at Embers' to get the terminal diagnosis? Like this doesn't take a genius to rewrite the story, V would still have motivation to remove virus from his head but wouldn't be in constant rush.
Another way I've always thought - just don't have Viktor say "two weeks, tops," have it more indeterminate ("could be a few weeks, a few months, maybe even a year, impossible to say with tech like this, you might be able to fight it off some with these pills, but I can't say how long for") and don't have Goro contacting V in the cafe till a much later trigger, with the hallucinations starting to intrude more to the extent that you're feeling the crisis looming closer. You could even have the staving-off effect of the pills you're taking be more prominent, like part of the gameplay (They're hard to get and you have to source them from underground criminals or something). (In fact, the pills should have served that staving-off purpose, they're introduced like that when Misty gives them to you, but the theme doesn't appear again.)
Bingo, you have a much more immersive and suspension-of-disbelief-continuing excuse to explore the city after the heist, look for some of the other clues and build up rep for a while (even though the exploring and rep-building should have been the bulk of the early to mid game, and the whole heist/chip thing the beginning of the endgame, but that would require too much re-jigging).
It's the same as the Bethesda shit - a supposedly urgent MQ that's inexplicably not actually urgent, just so you can have an excuse to explore the world. It's silly that they have to have atemporal workarounds like the fact that you can agree to meet Goro at the waterfront and leave him hanging there for as long as you like - it's just ridiculous. By that stage there should be more urgency and momentum to the thing.