I can't wrap my head around it so if someone could explain this to me. According to http://www.vncbearing.com/roller-bearings-vs-ball-bearings-major-differences/ ball bearings can handle thrust loads but roller bearings can't. Now I understand that ball can rotate around all axis and roller around only one, but still... If you put a shaft on those bearings it's meant to rotate, you don't allow a shaft to go through a bearing, it's always fixated in one way or another. So what's really the point of that statement?
if you look at a ball bearing in cross-section, you will see that the balls are assembled into the two races in such a way that the races have side walls against which the balls can press as they roll. this means that a thrust load on one race will be transmitted through the balls to the opposite race without tending to push the races apart and open up the bearing. note that to assemble the bearing, one of the sidewalls on one of the races has to be missing its sidewall so the balls can be inserted between the races, so the bearing's ability to sustain thrust loads in one direction will be limited by that. But a roller bearing's races do not have sidewalls that can carry thrust loads without scuffing the ends of the rollers against other parts of the bearing and thereby galling and/or grinding those parts into failure.
Your main assumption,
If you put a shaft on those bearings it's meant to rotate, you don't allow a shaft to go through a bearing, it's always fixated in one way or another
does not hold true in many cases. For example the only thing that keeps a bicycle wheel from sliding around are the bearings (if anything but the ball bearing, you'd have a sliding point of contact which would mean more friction and wear). Another example is the free spinning carriage wheel axle set that was the need fulfilled by the Timken roller bearing (p 18). Rollers can take a much heavier load than balls. Until then that required a set of radial bearings and another set of thrust bearings. If simple roller bearings take an axial load the ends of the cylinders are sliding against the cage with force. Timken angled the profile of the bearing to make it be used with another like a pair of opposing angular ball bearings, but the key to that was making them tapered. A plain cylinder can't roll in a circle on a cone without sliding a little over much of it's length. So the races and the cylinders all tapered to the same point allowing all the parts to roll together.
Even when you throw an engine in the middle of that axle (a car) that's connected to the frame as is the outer race of your wheel bearing you don't want all the axial forces from the wheels taken up by expensive parts in the transmission. You still want the bearing to handle that.
Deep groove radial ball bearings can take axial force. The balls can roll slightly in the groove which takes the axial force. Angling the groove allows it to take more thrust in that direction. There are simple diagrams in this Nachi training guide showing the relative loads different bearing designs can handle.