Why is Android phones' RAM capacity catching up with or even overtaking PCs'? In the past few years the RAM capacity of Android phones have rised by a lot. A typically average Android phone has 1GB RAM in 2013, but 4GB in 2017. Comparing with PCs, the typical RAM capacity has only rised from 2GB to 4GB. Even 8GB phones start to show up.

This is somewhat unreasonable, at least to me. Because:


Phones and tablets are rarely used for "intensive productivity" like editing large photos, applying post FX to videos, doing 3D model building and so on.  
Heavy gaming hasn't yet been possible due to other limitations (i.e. CPU &amp; GPU). You want COD: Black Ops III on a phone?  
Dual channel RAM is almost twice as fast as single-channel, but unlike RAID disks, this has nothing to do with capacity.  


So why? How is such RAM capacity useful?
It depends on screen size and pixel density - so the minimum for 32 bit is close to 1.5 GB for 32 bit 2GB for 64 bit at the highest end - Section 7.6.1 of android Compatibility Definition
This size is only for the OS , radio (modem) is extra, which is not much anyway.
As discussed in this question 2 GB RAM or 3 GB RAM, does it really matter?, RAM requirements from OS per se are not high but as pointed out by Andy Yan in his answer - apps occupying more RAM with usage and apps with increasing functionalities (WhatsApp for instance ) tend to grow in size


But coming to your question, why in Android and why not in PCs , IMO, factors which are unique to Android


Multiple apps being open especially social apps in addition to standards mail, messaging , maps etc can lead to some apps being killed as RAM is less (not so on PCs) - poor user experience
Future platform releases - 4GB is strongly recommended ( see last section of CDD linked above ) . Compare with Windows minimum requirements - RAM: 1 gigabyte (GB) (32-bit) or 2 GB (64-bit). For Linux it would be far less 
Selling point, whether it matters in reality or not (on a 5 inch screen does HD make a difference ? Not to me, at least )