Speed Calculations

But why SOLAS requires ship's to use STW for collision avoidance?

We go back in time, again. It was important to know speed and course of another vessel to assess alteration of own ship. And at that time it was Water speed and heading.
Why? Because GPS is much younger than Radar and Water Log.
The action was planned. It is easy to monitor slight change of CPA between several targets at same time now. It is all calculated by ARPA once echo is acquired.
Nobody calculates the required alteration. The course is changed until needed CPA or BCR is met.
What will the difference of true vector be depending on STW or SOG chosen?
Based on STW calculations results will give speed of targets in stationery water. The water without current. It is ok in open waters.
It will also give some confusing results in confined waters. Such as indication of moving light houses and small islands, which are fixed to the ground. That would be observed if Water Log is not accurate and/or there is a strong current.
On the other hand it will help to determine real current as it will be of opposite direction as shown for fixed object. But same speed.
I would say that use of SOG is more logic in confined waters. Many pilots prefer to have it on the screen. 

My personnal opinion about the state of STW in International regulation is simple. Old tradition and belief that satelite navigation is still unreliable. I do not think Dynamic Positioning agrees with the later. 

Here is a small sketch. Maybe some vectors point in wrong direction. But that would confuse people unfamiliar with vectors at all.
A1 – own vector. STW 
A2 - target's vector. STW
B1 – own SOG.
B2 target's SOG.
C – current.
D – relative vector.