Before I answer, let me start by saying that you can't see the European powers as some kind of monolith that had a unified vision of what to do with the New World. Instead, many different countries and non-state actors all had their own reasons for attempting to colonize the New World and their own ways of profiting off of the new world trade system. With that out of the way, the question becomes why it wasn't more common for Europeans to colonize the New World themselves to profit off of the Americas.

Firstly, you should consider that colonizing the New World was a risky and expensive endeavour. Travelling by sea was dangerous, especially if you're shipping a bunch of poor people cramped together in a time before hygiene or knowledge of bacteria. It would be hard to convince a peasant to leave their lives behind to embark on this uncertain adventure, which is why a lot of early settlers to North America were either forced to as prisoners, or had been part of persecuted minorities and thought the promise of religious freedom was worth the risk.

Another important reason is the economic strength of the Atlantic triangular trade system. The use of slaves meant not only that they had a cheap and plentiful labor force to cultivate these new lands for cash crops, they also had an extra market to sell European goods. This meant ships could cycle between the Americas, Africa and Europe while benefitting the Europeans at each stop. Loading a ship full of your own subjects to drop off as a labor force would just not be as good an investment as buying a bunch of slaves with that money and keeping your subjects in Europe as a labor force for those sweet imported cash crops.

That's not to say Europeans didn't settle elsewhere out of free will, but the cash crops that made the New World so profitable were very labor intensive, making the return on investment small if you send out your own colonists with the sole purpose of growing those cash crops. But if you add cheap slave labor to the mix, suddenly investments become much more attractive. This way, relatively few European subjects were needed, leaving most of the risk of actually colonizing and working the lands to what was viewed as disposable slave labor, while various, relatively small European groups colonized certain places all over the world to profit off of this new trade.

In summation, it was much more profitable and less risky for Europeans to stay home and earn money by working on the freshly imported crops, which would have been too labor-intensive to cheaply import if not for slave labor.