So from schematics or youtube it is clear that car electric starter is connected to battery positive terminal with two connections: one is always connected to battery (B wire) and one going through ignition switch, relay, park-neutral switch and so on (S wire). My question is why both are needed - can't we create a starter with only S wire (for example I cut B wire at some place altogether, and connect both B and S log nuts with crocodile clip)? Is it because there some larger current through B wire and it needs thicker cables? Or current at startup is the same through both wires and there is some other reason?
There are two connections because the current to drive the starter is high so it has a direct supply from the battery and the other connection is the control.
The connection through the ignition switch, park switch then solenoid is for two reasons:
To operate the starter when it is safe to do so ie not in gear
The starter needs a high current (in excess of 250 or 300A and sometimes a lot more), so the solenoid switches that high current once the teeth are engaged - part of the function of the solenoid is to move the pinion into engagement with the flywheel.
Based on the image added, then it is possible to put a different relay in place of the existing starter relay (capable of 300A or so) and link the two connections on the starter. This is not done as it does not add any functionality and just costs more since it just duplicates the function of the solenoid fitted to the starter itself.
The starter system on many small cars used to be done the way you describe, and on small engines, like lawn tractors, still is. The high current was switched by a special heavy duty relay (it's denoted as a solenoid in the diagram below). The starters used in this configuration were known as inertia-engagement starters, and had a drive mechanism that screwed itself into mesh with the ring gear along a helical spline as the motor accelerated up to speed. Although this works well enough when everything is in good condition, wear and dirt accumulating on the drive mechanism can cause failure to engage properly, and then you hear a loud grinding noise as the pinion spins against the edge of the ring gear - which damages both ring and pinion and makes future engagements even less likely to be successful.
On modern engines, the expectation for reliable operation over a long life has led to the use of pre-engaged starters, which have a solenoid on the side of the motor that pushes the pinion into mesh via a shift lever (actuating arm). This means that there is a solenoid that can be used to operate the high current contacts for the motor current present - which means that the separate high current relay isn't needed, the starter relay in your diagram is just a cheap cube relay. There's another advantage - the shifting mechanism can be designed such that the contacts close only when the pinion is definitely engaged, reducing the possibility of the gears grinding against each other. That then is the main reason why there are two separate feeds to the starter - you don't want to have a second high current relay switching the entire feed when it can be done with a contact set built into the shifting solenoid - it would add more expense to the system than saving the separate wire to the starter solenoid. Images from here