So with a SIG/PWR/GND/SIG arrangement (PWR is green):



... couldn't I delete the ground sections like this (because of the ground layer):

 

I've got a mic project where there is GND, and there is Virtual GND.

In a 4 layer, could I do one of the inner layers as GND and the other as VGND? I tried in EasyEDA, but it thinks both planes are GND.

 

couldn't I delete the ground sections like this

Yes, you can. BUT:
VIAs are not perfect. They have some resistance and inductance. They also have some max current. Sometimes they do not connect, not often!
The point of capacitors on an IC (voltage regulator for example) is to connect the power pin back to the ground pin in a very short and direct route. (low resistance and low inductance)

I do the top picture to make all the loops short, direct and local. I like that you connect the Ground of U7 to the Ground plane with several VIAs.
This appears to be a voltage regulator, and it will produce heat. The heat gets away by copper. The more copper you add (and the more VIAs you add close) the lower the temperature.

 

What about this? related to Post 21, 23
(red top layer, green inner power layer)




Also in EasyEDA, you can make the ground pad DIRECT (IC8), instead of SPOKE (C16, C17). This should do heat dissipation better.

 

FWIW I always put GND as the top layer so no vias needed to ground anything and being outside it gets heat away better.

 

I wouldn’t expect there to be traces on inner layers…just via connection. Both inner layers are planes. Top and bottom layer are signal/trace layers.

 

Also in EasyEDA, you can make the ground pad DIRECT (IC8)

I don't know EasyEDA. In most CADs you can edit options on the pad. "Spokes" at 90 degrees or 45 degrees or 2 vs 4. Try all the options. I think there is one for "no thermals". I am certain the wording will be strange. We all speak a different language.