Packet loss is the proper explanation.
What happens is that sometimes the signal between the wireless router and and console will just not be good enough to keep communication going at 60 frames a second (or whatever the rate is). What happens then is that the console goes “Hey wait a second, I didn’t get any info from my opponent for this next frame” and requests it again. That’s why the game pauses for just a brief period. If it happens enough, the game then says “Well, let’s try getting the information even further in advance to smooth things out”, and the input delay increases.
Since a wired connection doesn’t have those signal issues, the console can keep the delay as small as possible, making the experience much better.
Yeah, I know it’s annoying running cable between various rooms. But when I was a decent distance from my router/modem, I did it (PC player here). You should be able to find cable anchors you can hammer into the wall (along with couplers for easy disconnection) if that’s an issue.