What prevents people from manipulating data to write better papers?

Can I use what I described above to publish a paper without much hassle?

Yes, it's easy to write a fraudulent paper, and it's not hard to get it published if you are willing to publish in a journal with low standards. (Some predatory publishers will publish literally anything if you are willing to pay them.) You might even get it published somewhere respectable if you fake everything convincingly, by getting results that are good enough to be impressive without being so implausible that reviewers become suspicious.

Is there something I am missing?

I'd bet that what you're missing is the role of reputation in academia. If you don't maintain a good reputation, you'll be ignored and marginalized, with no ability to influence the field. If your only goal is to produce a paper, then there's a lot of scope for mischief, but this generally won't lead to a successful research career. If people are unable to build on your work, they'll become suspicious and your reputation will suffer. (And if they aren't even interested in trying to build on your work, then by definition you aren't having an influential career.)

It's not impossible to succeed in academia by fraud, as demonstrated by the people who succeeded for some years before they were caught. However, it's much harder than faking a single paper.

What prevents people from doing this? Is there something I'm missing?

In addition to the factors mentioned in Anonymous Mathematician's excellent answer, I think another factor at play is that while it is not very difficult for a dishonest person to (temporarily) get ahead by faking data, the rewards for doing it aren't very great compared to the effort it takes to implement this strategy successfully. Even the barrier to entry in academia, getting a PhD, is high enough to deter the most dishonest people, who are the kinds of people who may be tempted to use fraudulent strategies to attain professional success, money etc. And the payoff for this kind of fraud is ultimately quite modest -- you might get a job with tenure, but is that really worth the trouble of working on something you have no real passion for, and doing so in a dishonest way, for so many years?

The bottom line is that Academia is simply not an attractive place for fraudsters, certainly much less attractive than other industries or career tracks (which I won't name) where fraud and other antisocial behavior can reap you much greater rewards in a much shorter period of time. So yes, a hypothetical fraudster who ends up in academia can gain some traction in their career using dishonest methods (until they are caught at least), and occasionally we hear stories about such people. But these stories are rare precisely because academic research as a career option is most appealing to people who by and large are passionate about advancing human knowledge, and therefore are not predisposed to committing major acts of scientific fraud.

An example is Jan Hendrik Schön. He manipulated data on a big scale. But after people found out about it, he lost his job (and academic career) and even got stripped of his doctor title.

Apart from this, I guess that most scientists are actually interested in honest academic research (i.e. finding out something truly new) and not in a career build on lies. Moreover, many scientists suffer from some other extreme, they believe that they are imposters (while producing valid science).