It depends what you mean by "tend to create".
For one, there are certain words that do tend to be the same across unrelated languages—for external reasons.
- English boom and Ancient Greek bómbos look very similar, because they're both imitating the same sound.
- Quite a lot of languages have a word for "mother" that sounds like mama, because
/a/ are generally the first sounds babies are able to produce.
- Language contact can cause previously-unrelated words to become more similar over time, like how native English island gained an S by comparison with the unrelated French borrowing isle.
You ask specifically, though, if false cognates are "more frequent than chance". And while I don't know of any studies specifically on this topic, I suspect the answer is no.
In other words, languages do tend to have very large numbers of false cognates! But the frequency is pretty close to what we'd expect just due to random chance. Humans just have a tendency to focus on the similarities and overlook the differences, and to underestimate just how many words a language has. Mark Rosenfelder does some analysis on this (in the context of evaluating claims that languages are related) and predicts several hundred false cognates between any two random languages.
I'm not sure if any formal studies have been done on this, and if you're interested, it might be a good area to research: take corpora for various different languages, find a good measure of similarity, and see how often false cognates appear. But my prediction is that the rate will be very similar to what you'd expect from random chance.