And you'll notice that pretty much all the hue and cry over "this is bad" is almost never backed up by actual play experience.
Nah. That's not true.
"This is bad" is usually (say, 65% of the time) completely backed up by actual play experience. It's much rarer when it's not. The problematic issue that some people will never, ever, ever, ever, ever, ever, ever admit some element of a game they like is
actually bad unless it's so satanically bad it basically ruins the entire game, and instead of wanting to "improve the game somewhat", will defend to the death anything, not matter how terrible, so long as it doesn't completely sink the game. At best they'll equivocate about how some people might see X as bad but they see X as pretty okay or the like.
Luckily game designers tend to be a bit more sensible than that, and generally do attempt to get rid of minor, moderate and serious flaws as well as the killer ones no-one can ignore. It's always funny when they do remove something a bunch of people decided to defend as "X is okay, actually", because usually 9 in 10 of those people suddenly agree with the game designer that it wasn't great. Hmmmm. Such is human life.
Play-testing is vitally important because it turns up a ton of issues theorycrafting never will spot, not because it "DISPROVES!!!!!!" theorycrafting - it rarely does. But theorycrafting misses so many real issues that turn up in real games - or sometimes a small number of people might realize they're an issue, but not many, and then playtesting will show they're a big issue.
One particular place play-testing is vital is flow - it's very rare that you're able to really get how something flows, gameplay-wise, from reading the rules. Play-testing is pretty bad at spotting anything but gross balance issues, however, without the assistance of actual analysis, because player skill, specific situations/adventures, DM habits and so on can easily obscure significant balance issues unless what we're calling theorycraft has prepared the ground.
TLDR: They're both vital to making a complex RPG like 5E work, and neglecting one or the other is a mistake, as is focusing on the rather silly idea of "disproving" stuff through play-testing, rather than using theorycraft to inform play-testing, and play-testing to inform future analysis.